JEE Main & Advanced Mathematics Sequence & Series Question Bank

done Arithmetic Progression Total Questions - 102

• question_answer1)
  The sequence \[\frac{5}{\sqrt{7}}\], \[\frac{6}{\sqrt{7}}\], \[\sqrt{7}\], ....... is
  A)
  H.P. done clear
  B)
  G.P. done clear
  C)
  A.P. done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  pth  term of the series\[\left( 3-\frac{1}{n} \right)+\left( 3-\frac{2}{n} \right)+\left( 3-\frac{3}{n} \right)+....\] will be
  A)
  \[\left( 3+\frac{p}{n} \right)\] done clear
  B)
  \[\left( 3-\frac{p}{n} \right)\] done clear
  C)
  \[\left( 3+\frac{n}{p} \right)\] done clear
  D)
  \[\left( 3-\frac{n}{p} \right)\] done clear
  View Solution play_arrow

• question_answer3)
  8th term of the series \[2\sqrt{2}+\sqrt{2}+0+.....\] will be
  A)
  \[-5\sqrt{2}\] done clear
  B)
  \[5\sqrt{2}\] done clear
  C)
  \[10\sqrt{2}\] done clear
  D)
  \[-10\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer4)
  If the 9th term of an A.P. be zero, then the ratio of its  29th  and 19th  term is
  A)
  1 : 2 done clear
  B)
  2 : 1 done clear
  C)
  1 : 3 done clear
  D)
  3 : 1 done clear
  View Solution play_arrow

• question_answer5)
  Which of the following sequence is an arithmetic sequence
  A)
  \[f(n)=an+b;\,n\in N\] done clear
  B)
  \[f(n)=k{{r}^{n}};\,n\in N\] done clear
  C)
  \[f(n)=(an+b)\,k{{r}^{n}};\,n\in N\] done clear
  D)
  \[f(n)=\frac{1}{a\left( n+\frac{b}{n} \right)};\,n\in N\] done clear
  View Solution play_arrow

• question_answer6)
  Which term of the sequence \[(-8+18i),\,(-6+15i),\] \[(-4+12i)\]\[,......\]is purely imaginary
  A)
  5th done clear
  B)
  7th done clear
  C)
  8th done clear
  D)
  6th done clear
  View Solution play_arrow

• question_answer7)
  If the \[{{n}^{th}}\] term of an A.P. be \[(2n-1)\], then the sum  of its first \[n\] terms will be
  A)
  \[{{n}^{2}}-1\] done clear
  B)
  \[{{(2n-1)}^{2}}\] done clear
  C)
  \[{{n}^{2}}\] done clear
  D)
  \[{{n}^{2}}+1\] done clear
  View Solution play_arrow

• question_answer8)
  The \[{{n}^{th}}\] term of the following series \[(1\times 3)+(3\times 5)+(5\times 7)+(7\times 9)+.......\] will be
  A)
  \[n\,(2n+1)\] done clear
  B)
  \[2n\,(2n-1)\] done clear
  C)
  \[(2n+1)(2n-1)\] done clear
  D)
  \[4{{n}^{2}}+1\] done clear
  View Solution play_arrow

• question_answer9)
  The number of terms in the series \[101+99+97+.....+47\] is
  A)
  25 done clear
  B)
  28 done clear
  C)
  30 done clear
  D)
  20 done clear
  View Solution play_arrow

• question_answer10)
  If the \[{{p}^{th}}\] term of an A.P. be \[q\]  and \[{{q}^{th}}\]term be p, then its \[{{r}^{th}}\] term will be [RPET 1999]
  A)
  \[p+q+r\] done clear
  B)
  \[p+q-r\] done clear
  C)
  \[p+r-q\] done clear
  D)
  \[p-q-r\] done clear
  View Solution play_arrow

• question_answer11)
  If \[\tan \,n\theta =\tan m\theta \], then the different values of will be in [Karnataka CET 1998]
  A)
  A.P. done clear
  B)
  G.P. done clear
  C)
  H.P. done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  \[{{n}^{th}}\] term of the series  \[3.8+6.11+\] \[9.14+12.17+.....\]will be
  A)
  \[3n(3n+5)\] done clear
  B)
  \[3n(n+5)\] done clear
  C)
  \[n(3n+5)\] done clear
  D)
  \[n(n+5)\] done clear
  View Solution play_arrow

• question_answer13)
  The sum of integers from 1 to 100 that are divisible by 2 or 5 is [IIT 1984]
  A)
  3000 done clear
  B)
  3050 done clear
  C)
  4050 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  If . terms of the series \[63+65+67+69+.........\] and \[3+10+17+24+......\] be equal, then [Kerala (Engg.) 2002]
  A)
  11 done clear
  B)
  12 done clear
  C)
  13 done clear
  D)
  15 done clear
  View Solution play_arrow

• question_answer15)
  The sum of 24 terms of the following series \[\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+.........\] is
  A)
  300 done clear
  B)
  \[300\sqrt{2}\] done clear
  C)
  \[200\sqrt{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  If \[2x,\ x+8,\ 3x+1\] are in A.P., then the value of \[x\] will be  [MP PET 1984]
  A)
  3 done clear
  B)
  7 done clear
  C)
  5 done clear
  D)
  - 2 done clear
  View Solution play_arrow

• question_answer17)
  If the sum of \[n\] terms of an A.P. is \[nA+{{n}^{2}}B\], where \[A,B\] are constants, then its common difference will be [MNR 1977]
  A)
  \[A-B\] done clear
  B)
  \[A+B\] done clear
  C)
  \[2A\] done clear
  D)
  \[2B\] done clear
  View Solution play_arrow

• question_answer18)
  If the \[{{9}^{th}}\] term of an A.P. is 35  and  is 75, then its \[{{20}^{th}}\] terms will be  [RPET 1989]
  A)
  78 done clear
  B)
  79 done clear
  C)
  80 done clear
  D)
  81 done clear
  View Solution play_arrow

• question_answer19)
  The \[{{9}^{th}}\] term of the series \[27+9+5\frac{2}{5}+3\frac{6}{7}+........\] will be  [MP PET 1983]
  A)
  \[1\frac{10}{17}\] done clear
  B)
  \[\frac{10}{17}\] done clear
  C)
  \[\frac{16}{27}\] done clear
  D)
  \[\frac{17}{27}\] done clear
  View Solution play_arrow

• question_answer20)
  If \[a,\ b,\ c\] are in A.P., then \[\frac{{{(a-c)}^{2}}}{({{b}^{2}}-ac)}=\] [Roorkee 1975]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer21)
  . If \[{{\log }_{3}}2,\ {{\log }_{3}}({{2}^{x}}-5)\] and \[{{\log }_{3}}\left( {{2}^{x}}-\frac{7}{2} \right)\] are in A.P., then \[x\] is equal to [IIT 1990]
  A)
  \[1,\ \frac{1}{2}\] done clear
  B)
  \[1,\ \frac{1}{3}\] done clear
  C)
  \[1,\ \frac{3}{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer22)
  If the \[{{p}^{th}},\ {{q}^{th}}\] and \[{{r}^{th}}\] term of an arithmetic sequence are a , b and \[c\] respectively, then the value of \[[a(q-r)\] + \[b(r-p)\] \[+c(p-q)]=\] [MP PET 1985]
  A)
  1 done clear
  B)
  \[-1\] done clear
  C)
  0 done clear
  D)
  1/2 done clear
  View Solution play_arrow

• question_answer23)
  If \[{{n}^{th}}\]  terms of two A.P.'s are \[3n+8\] and \[7n+15\], then the ratio of their \[{{12}^{th}}\] terms will be  [MP PET 1986]
  A)
  4/9 done clear
  B)
  7/16 done clear
  C)
  3/7 done clear
  D)
  8/15 done clear
  View Solution play_arrow

• question_answer24)
  If \[{{a}_{1}}={{a}_{2}}=2,\ {{a}_{n}}={{a}_{n-1}}-1\ (n>2)\], then \[{{a}_{5}}\]is
  A)
  1 done clear
  B)
  \[-1\] done clear
  C)
  0 done clear
  D)
  \[-2\] done clear
  View Solution play_arrow

• question_answer25)
  If the numbers \[a,\ b,\ c,\ d,\ e\] form an A.P., then the value of \[a-4b+6c-4d+e\] is
  A)
  1 done clear
  B)
  2 done clear
  C)
  0 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  The sixth term of an A.P. is equal to 2, the value of the common difference of the A.P. which makes the product \[{{a}_{1}}{{a}_{4}}{{a}_{5}}\] least is given by
  A)
  \[x=\frac{8}{5}\] done clear
  B)
  \[x=\frac{5}{4}\] done clear
  C)
  \[x=2/3\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer27)
  If \[p\]times the \[{{p}^{th}}\] term of an A.P. is equal to \[q\] times the \[{{q}^{th}}\] term of an A.P., then \[{{(p+q)}^{th}}\] term is [MP PET 1997; Karnataka CET 2002]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer28)
  The sums of  terms of two arithmatic series are in the ratio  \[2n+3:6n+5\], then the ratio of their \[{{13}^{th}}\] terms is     [MP PET 2004]
  A)
  53 : 155 done clear
  B)
  27 : 77 done clear
  C)
  29 : 83 done clear
  D)
  31 : 89 done clear
  View Solution play_arrow

• question_answer29)
  If am denotes the mth term  of an A.P. then am = 
  A)
  \[\frac{2}{{{a}_{m+k}}+{{a}_{m-k}}}\] done clear
  B)
  \[\frac{{{a}_{m+k}}-{{a}_{m-k}}}{2}\] done clear
  C)
  \[\frac{{{a}_{m+k}}+{{a}_{m-k}}}{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
   Let \[{{T}_{r}}\] be the \[{{r}^{th}}\] term of an A.P. for \[r=1,\ 2,\ 3,....\]. If for some positive integers \[m,\ n\] we have \[{{T}_{m}}=\frac{1}{n}\] and \[{{T}_{n}}=\frac{1}{m}\], then  equals [IIT 1998]
  A)
  \[\frac{1}{mn}\] done clear
  B)
  \[\frac{1}{m}+\frac{1}{n}\] done clear
  C)
  1 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer31)
  If \[1,\,\,{{\log }_{9}}({{3}^{1-x}}+2),\,\,{{\log }_{3}}({{4.3}^{x}}-1)\] are in A.P. then x  equals [AIEEE 2002]
  A)
  \[{{\log }_{3}}4\] done clear
  B)
  \[1-{{\log }_{3}}4\] done clear
  C)
  \[1-{{\log }_{4}}3\] done clear
  D)
  \[{{\log }_{4}}3\] done clear
  View Solution play_arrow

• question_answer32)
  If \[a,b,c,d,e\] are in A.P. then the value of \[a+b+4c\] \[-4d+e\]  in terms of a, if possible is [RPET 2002]
  A)
  4a done clear
  B)
  2a done clear
  C)
  3 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer33)
  If the ratio of the sum of \[n\] terms of two A.P.'s be \[(7n+1):(4n+27)\], then the ratio of their \[{{11}^{th}}\] terms will be [AMU 1996]
  A)
  \[2:3\] done clear
  B)
  \[3:4\] done clear
  C)
  \[4:3\] done clear
  D)
  \[5:6\] done clear
  View Solution play_arrow

• question_answer34)
  The sum of the series \[\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+........\]to 9  terms is [MNR 1985]
  A)
    \[-\frac{5}{6}\] done clear
  B)
  \[-\frac{1}{2}\] done clear
  C)
    1 done clear
  D)
  \[-\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer35)
  The interior angles of a polygon are in A.P. If the smallest angle be \[{{120}^{o}}\] and the common difference be 5o, then the number of sides is [IIT 1980]
  A)
  8 done clear
  B)
  10 done clear
  C)
  9 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer36)
  If the \[{{p}^{th}}\] term of an A.P. be \[\frac{1}{q}\] and \[{{q}^{th}}\] term be\[\frac{1}{p}\], then the sum of its \[p{{q}^{th}}\]terms will be
  A)
  \[\frac{pq-1}{2}\] done clear
  B)
  \[\frac{1-pq}{2}\] done clear
  C)
  \[\frac{pq+1}{2}\] done clear
  D)
  \[-\frac{pq+1}{2}\] done clear
  View Solution play_arrow

• question_answer37)
  The sum of first \[n\] natural numbers is [MP PET  1984; RPET 1995]
  A)
  \[n\,(n-1)\] done clear
  B)
  \[\frac{n\,(n-1)}{2}\] done clear
  C)
  \[n\,(n+1)\] done clear
  D)
  \[\frac{n\,(n+1)}{2}\] done clear
  View Solution play_arrow

• question_answer38)
  The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be [MNR 1978; MP PET 2002]
  A)
  3200 done clear
  B)
  1600 done clear
  C)
  200 done clear
  D)
  2800 done clear
  View Solution play_arrow

• question_answer39)
  If \[n\] be odd or even, then the sum of \[n\] terms of the series \[1-2+\] \[3-\]\[4+5-6+......\] will be
  A)
  \[-\frac{n}{2}\] done clear
  B)
  \[\frac{n-1}{2}\] done clear
  C)
  \[\frac{n+1}{2}\] done clear
  D)
  \[\frac{2n+1}{2}\] done clear
  View Solution play_arrow

• question_answer40)
  If the first, second and last terms of an A.P. be \[a,\ b,\ 2a\] respectively, then its sum will be
  A)
  \[\frac{ab}{b-a}\] done clear
  B)
  \[\frac{ab}{2(b-a)}\] done clear
  C)
  \[\frac{3ab}{2(b-a)}\] done clear
  D)
  \[\frac{3ab}{4(b-a)}\] done clear
  View Solution play_arrow

• question_answer41)
  The ratio of the sums of first \[n\] even numbers and \[n\] odd numbers will be
  A)
  \[1:n\] done clear
  B)
  \[(n+1):1\] done clear
  C)
  \[(n+1):n\] done clear
  D)
  \[(n-1):1\] done clear
  View Solution play_arrow

• question_answer42)
  If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}}.......{{a}_{n}}\] are in A.P., where \[{{a}_{i}}>0\] for all \[i\], then the value of\[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\] \[........+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}=\] [IIT 1982]
  A)
  \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\] done clear
  B)
  \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\] done clear
  C)
  \[\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\] done clear
  D)
  \[\frac{n+1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\] done clear
  View Solution play_arrow

• question_answer43)
  If \[{{a}_{1}},\ {{a}_{2}},............,{{a}_{n}}\] are in A.P. with common difference , \[d\], then the sum of the following series is \[\sin d(\cos \text{ec}\,{{a}_{1}}.co\text{sec}\,{{a}_{2}}+\text{cosec}\,{{a}_{2}}.\text{cosec}\,{{a}_{3}}+...........\]\[+\text{cosec}\ {{a}_{n-1}}\text{cosec}\ {{a}_{n}})\] [RPET 2000]
  A)
  \[\sec {{a}_{1}}-\sec {{a}_{n}}\] done clear
  B)
  \[\cot {{a}_{1}}-\cot {{a}_{n}}\] done clear
  C)
  \[\tan {{a}_{1}}-\tan {{a}_{n}}\] done clear
  D)
  \[c\text{osec}\ {{a}_{1}}-\text{cosec}\ {{a}_{n}}\] done clear
  View Solution play_arrow

• question_answer44)
  If the sum of the series \[2+5+8+11............\]is 60100, then the number of terms are [MNR 1991; DCE 2001]
  A)
  100 done clear
  B)
  200 done clear
  C)
  150 done clear
  D)
  250 done clear
  View Solution play_arrow

• question_answer45)
  The sum of all natural numbers between 1 and 100 which are multiples of 3 is [MP PET 1984]
  A)
  1680 done clear
  B)
  1683 done clear
  C)
  1681 done clear
  D)
  1682 done clear
  View Solution play_arrow

• question_answer46)
  The sum of \[1+3+5+7+.........\]upto \[n\] terms is  [MP PET 1984]
  A)
  \[{{(n+1)}^{2}}\] done clear
  B)
  \[{{(2n)}^{2}}\] done clear
  C)
  \[{{n}^{2}}\] done clear
  D)
  \[{{(n-1)}^{2}}\] done clear
  View Solution play_arrow

• question_answer47)
  If the sum of the series \[54+51+48+.............\] is 513, then the number of terms are  [Roorkee 1970]
  A)
  18 done clear
  B)
  20 done clear
  C)
  17 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer48)
  If the sum of \[n\] terms of an A.P. is \[2{{n}^{2}}+5n\], then the \[{{n}^{th}}\] term will be [RPET 1992]
  A)
  \[4n+3\] done clear
  B)
  \[4n+5\] done clear
  C)
  \[4n+6\] done clear
  D)
  \[4n+7\] done clear
  View Solution play_arrow

• question_answer49)
  The \[{{n}^{th}}\] term of an A.P. is \[3n-1\].Choose from the following the sum of its first five terms [MP PET 1983]
  A)
  14 done clear
  B)
  35 done clear
  C)
  80 done clear
  D)
  40 done clear
  View Solution play_arrow

• question_answer50)
  If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are [RPET 1987]
  A)
  5 done clear
  B)
  8 done clear
  C)
  10 done clear
  D)
  15 done clear
  View Solution play_arrow

• question_answer51)
  The maximum sum of the series \[20+19\frac{1}{3}+18\frac{2}{3}+.........\] is
  A)
  310 done clear
  B)
  300 done clear
  C)
  320 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  The sum of the numbers between 100 and 1000 which is divisible by 9 will be [MP PET 1982]
  A)
  55350 done clear
  B)
  57228 done clear
  C)
  97015 done clear
  D)
  62140 done clear
  View Solution play_arrow

• question_answer53)
  The ratio of sum of \[m\] and \[n\] terms  of an A.P. is \[{{m}^{2}}:{{n}^{2}}\], then the ratio of \[{{m}^{th}}\]and \[{{n}^{th}}\] term will be [Roorkee 1963; MP PET 1995; Pb. CET 2001]
  A)
  \[\frac{m-1}{n-1}\] done clear
  B)
  \[\frac{n-1}{m-1}\] done clear
  C)
  \[\frac{2m-1}{2n-1}\] done clear
  D)
  \[\frac{2n-1}{2m-1}\] done clear
  View Solution play_arrow

• question_answer54)
  The value of   \[\sum\limits_{r=1}^{n}{\log \left( \frac{{{a}^{r}}}{{{b}^{r-1}}} \right)}\] is
  A)
  \[\frac{n}{2}\log \left( \frac{{{a}^{n}}}{{{b}^{n}}} \right)\] done clear
  B)
  \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n}}} \right)\] done clear
  C)
  \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n-1}}} \right)\] done clear
  D)
  \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n+1}}} \right)\] done clear
  View Solution play_arrow

• question_answer55)
  The solution of the equation\[(x+1)+(x+4)+(x+7)+.........+(x+28)=155\] is 
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer56)
  The sum of all two digit numbers which, when divided by 4, yield unity as a remainder is
  A)
  1190 done clear
  B)
  1197 done clear
  C)
  1210 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer57)
  If \[{{S}_{n}}\] denotes the sum of \[n\] terms of an arithmetic progression, then the value of \[({{S}_{2n}}-{{S}_{n}})\] is equal to
  A)
  \[2{{S}_{n}}\] done clear
  B)
  \[{{S}_{3n}}\] done clear
  C)
    \[\frac{1}{3}{{S}_{3n}}\] done clear
  D)
    \[\frac{1}{2}{{S}_{n}}\] done clear
  View Solution play_arrow

• question_answer58)
  The solution of\[{{\log }_{\sqrt{3}}}x+{{\log }_{\sqrt[4]{3}}}x+{{\log }_{\sqrt[6]{3}}}x+.........+{{\log }_{\sqrt[16]{3}}}x=36\] is
  A)
  \[x=3\] done clear
  B)
  \[x=4\sqrt{3}\] done clear
  C)
  \[x=9\] done clear
  D)
  \[x=\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer59)
  If \[{{S}_{k}}\] denotes the sum of first \[k\]terms of an arithmetic progression whose first term and common difference are \[a\]and \[d\] respectively, then \[{{S}_{kn}}/{{S}_{n}}\] be independent of \[n\] if
  A)
  \[2a-d=0\] done clear
  B)
  \[a-d=0\] done clear
  C)
  \[a-2d=0\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer60)
  A series whose nth term is \[\left( \frac{n}{x} \right)+y,\]the sum of r  terms will be [UPSEAT 1999]
  A)
  \[\left\{ \frac{r(r+1)}{2x} \right\}+ry\] done clear
  B)
  \[\left\{ \frac{r(r-1)}{2x} \right\}\] done clear
  C)
  \[\left\{ \frac{r(r-1)}{2x} \right\}-ry\] done clear
  D)
  \[\left\{ \frac{r(r+1)}{2y} \right\}-rx\] done clear
  View Solution play_arrow

• question_answer61)
  The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is [MP PET 2000]
  A)
  2489 done clear
  B)
  4735 done clear
  C)
  2317 done clear
  D)
  2632 done clear
  View Solution play_arrow

• question_answer62)
  The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is [MP PET 2003]
  A)
  1 done clear
  B)
  8 done clear
  C)
  4 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer63)
  If the sum of the first 2n terms of \[2,\,5,\,8...\] is equal to the sum of the first n terms of \[57,\,59,\,61...\], then n is equal to [IIT Screening 2001]
  A)
  10 done clear
  B)
  12 done clear
  C)
  11 done clear
  D)
  13 done clear
  View Solution play_arrow

• question_answer64)
  The sum of numbers from 250 to 1000 which are divisible by 3 is [RPET 1997]
  A)
  135657 done clear
  B)
  136557 done clear
  C)
  161575 done clear
  D)
  156375 done clear
  View Solution play_arrow

• question_answer65)
  \[{{7}^{th}}\] term of an A.P. is 40, then the sum of first 13 terms is  [Karnataka CET 2003]
  A)
  53 done clear
  B)
  520 done clear
  C)
  1040 done clear
  D)
  2080 done clear
  View Solution play_arrow

• question_answer66)
  If \[{{a}_{1}},\,{{a}_{2}},....,{{a}_{n+1}}\] are in A.P., then \[\frac{1}{{{a}_{1}}{{a}_{2}}}+\frac{1}{{{a}_{2}}{{a}_{3}}}+.....+\frac{1}{{{a}_{n}}{{a}_{n+1}}}\] is [AMU 2002]
  A)
  \[\frac{n-1}{{{a}_{1}}{{a}_{n+1}}}\] done clear
  B)
  \[\frac{1}{{{a}_{1}}{{a}_{n+1}}}\] done clear
  C)
  \[\frac{n+1}{{{a}_{1}}{{a}_{n+1}}}\] done clear
  D)
  \[\frac{n}{{{a}_{1}}{{a}_{n+1}}}\] done clear
  View Solution play_arrow

• question_answer67)
  If the sum of the first  terms of a series be\[5{{n}^{2}}+2n\], then its second term is [MP PET 1996]
  A)
  7 done clear
  B)
  17 done clear
  C)
  24 done clear
  D)
  42 done clear
  View Solution play_arrow

• question_answer68)
  Let the sequence \[{{a}_{1}},{{a}_{2}},{{a}_{3}},.............{{a}_{2n}}\] form an A.P. Then \[a_{1}^{2}-a_{2}^{2}+a_{3}^{3}-.........+a_{2n-1}^{2}-a_{2n}^{2}=\]
  A)
  \[\frac{n}{2n-1}(a_{1}^{2}-a_{2n}^{2})\] done clear
  B)
  \[\frac{2n}{n-1}(a_{2n}^{2}-a_{1}^{2})\] done clear
  C)
  \[\frac{n}{n+1}(a_{1}^{2}+a_{2n}^{2})\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer69)
  If sum of \[n\] terms of an A.P. is \[3{{n}^{2}}+5n\] and \[{{T}_{m}}=164\] then \[m=\]           [RPET 1991, 95; DCE 1999]
  A)
  26 done clear
  B)
  27 done clear
  C)
  28 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer70)
  If \[{{S}_{n}}=nP+\frac{1}{2}n(n-1)Q\], where \[{{S}_{n}}\] denotes the sum of the first \[n\] terms of an A.P., then the common difference is [WB JEE 1994]
  A)
  \[P+Q\] done clear
  B)
  \[2P+3Q\] done clear
  C)
  \[2Q\] done clear
  D)
  \[Q\] done clear
  View Solution play_arrow

• question_answer71)
  Let \[{{S}_{n}}\]denotes the sum of \[n\] terms of an A.P. If \[{{S}_{2n}}=3{{S}_{n}}\], then ratio \[\frac{{{S}_{3n}}}{{{S}_{n}}}=\]   [MNR 1993; UPSEAT 2001]
  A)
  4 done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer72)
  The first term of an A.P. of consecutive integers is \[{{p}^{2}}+1\] The sum of \[(2p+1)\] terms of this series can be expressed as
  A)
  \[{{(p+1)}^{2}}\] done clear
  B)
  \[{{(p+1)}^{3}}\] done clear
  C)
  \[(2p+1){{(p+1)}^{2}}\] done clear
  D)
  \[{{p}^{3}}+{{(p+1)}^{3}}\] done clear
  View Solution play_arrow

• question_answer73)
  The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is
  A)
  10 done clear
  B)
  11 done clear
  C)
  12 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer74)
  The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is [Kerala (Engg.) 2002]
  A)
  5 done clear
  B)
  10 done clear
  C)
  12 done clear
  D)
  14 done clear
  View Solution play_arrow

• question_answer75)
  There are 15 terms in an arithmetic progression. Its first term is 5 and their sum is 390. The middle term is [MP PET 1994]
  A)
  23 done clear
  B)
  26 done clear
  C)
  29 done clear
  D)
  32 done clear
  View Solution play_arrow

• question_answer76)
  If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common difference is [RPET 1986]
  A)
  \[1:2\] done clear
  B)
  \[2:1\] done clear
  C)
  \[2:3\] done clear
  D)
  \[3:2\] done clear
  View Solution play_arrow

• question_answer77)
  Three number are in A.P. such that their sum is 18 and sum of their squares is 158. The greatest number among them is [UPSEAT 2004]
  A)
  10 done clear
  B)
  11 done clear
  C)
  12 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer78)
  If \[\frac{3+5+7+..........\text{to}\ n\ \text{terms}}{5+8+11+.........\text{to}\ 10\ \text{terms}}=7\], then the value of\[n\] is  [MNR 1983; Pb. CET 2000]
  A)
  35 done clear
  B)
  36 done clear
  C)
  37 done clear
  D)
  40 done clear
  View Solution play_arrow

• question_answer79)
  If \[{{A}_{1}},\,{{A}_{2}}\] be two arithmetic means between \[\frac{1}{3}\] and \[\frac{1}{24}\] , then their values are
  A)
  \[\frac{7}{72},\,\frac{5}{36}\] done clear
  B)
  \[\frac{17}{72},\,\frac{5}{36}\] done clear
  C)
  \[\frac{7}{36},\,\frac{5}{72}\] done clear
  D)
  \[\frac{5}{72},\,\frac{17}{72}\] done clear
  View Solution play_arrow

• question_answer80)
  If  \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\] be the A.M. of \[a\] and \[b\], then \[n=\] [MP PET 1995]
  A)
  1 done clear
  B)
  \[-1\] done clear
  C)
    0 done clear
  D)
    None of these done clear
  View Solution play_arrow

• question_answer81)
  A number is the reciprocal of the other. If the arithmetic mean of the two numbers be \[\frac{13}{12}\], then the numbers are
  A)
  \[\frac{1}{4},\ \frac{4}{1}\] done clear
  B)
  \[\frac{3}{4},\ \frac{4}{3}\] done clear
  C)
  \[\frac{2}{5},\ \frac{5}{2}\] done clear
  D)
  \[\frac{3}{2},\ \frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer82)
  If \[A\] be a arithmetic mean between two numbers and \[S\] be the sum of \[n\] arithmetic means between the same numbers, then
  A)
  \[S=n\,A\] done clear
  B)
  \[A=n\,S\] done clear
  C)
  \[A=S\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer83)
  The arithmetic mean of first n natural number [RPET 1986]
  A)
  \[\frac{n-1}{2}\] done clear
  B)
  \[\frac{n+1}{2}\] done clear
  C)
  \[\frac{n}{2}\] done clear
  D)
  \[n\] done clear
  View Solution play_arrow

• question_answer84)
  The sum of \[n\] arithmetic means between \[a\] and \[b\], is [RPET 1986]
  A)
  \[\frac{n(a+b)}{2}\] done clear
  B)
  \[n(a+b)\] done clear
  C)
  \[\frac{(n+1)(a+b)}{2}\] done clear
  D)
  \[(n+1)(a+b)\] done clear
  View Solution play_arrow

• question_answer85)
  After inserting \[n\] A.M.'s between 2 and 38, the sum of the resulting progression is 200. The value of  \[n\] is [MP PET 2001]
  A)
  10 done clear
  B)
  8 done clear
  C)
  9 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer86)
  The mean of the series \[a,a+nd,\,\,a+2nd\] is [DCE 2002]
  A)
  \[a+(n-1)\,d\] done clear
  B)
  \[a+nd\] done clear
  C)
  \[a+(n+1)\,d\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer87)
  If \[f(x+y,x-y)=xy\,,\] then the arithmetic mean of \[f(x,y)\] and \[f(y,x)\] is [AMU 2002, 05]
  A)
  \[x\] done clear
  B)
  \[y\] done clear
  C)
  0 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer88)
  If \[\log 2,\ \log ({{2}^{n}}-1)\] and \[\log ({{2}^{n}}+3)\] are in A.P., then  n =   [MP PET 1998; Karnataka CET  2000; Pb. CET 2001]
  A)
  5/2 done clear
  B)
  \[{{\log }_{2}}5\] done clear
  C)
  \[{{\log }_{3}}5\] done clear
  D)
  3/2 done clear
  View Solution play_arrow

• question_answer89)
  If the sum of two extreme numbers of an A.P. with four terms is 8 and product of remaining two middle term is 15, then greatest number of the series will be [Roorkee 1965]
  A)
  5 done clear
  B)
  7 done clear
  C)
  9 done clear
  D)
  11 done clear
  View Solution play_arrow

• question_answer90)
  If the sides of a right angled traingle are in A.P., then the sides are proportional to [Roorkee 1974]
  A)
  1: 2: 3 done clear
  B)
  2: 3: 4 done clear
  C)
  3: 4: 5 done clear
  D)
  4: 5: 6 done clear
  View Solution play_arrow

• question_answer91)
  Three numbers are in A.P. whose sum is 33 and product is  792, then the smallest number from these numbers is [RPET 1988]
  A)
  4 done clear
  B)
  8 done clear
  C)
  11 done clear
  D)
  14 done clear
  View Solution play_arrow

• question_answer92)
  If \[a,\ b,\ c,\ d,\ e,\ f\] are in A.P., then the value of \[e-c\] will be  [Pb. CET 1989, 91]
  A)
  \[2(c-a)\] done clear
  B)
  \[2(f-d)\] done clear
  C)
  \[2(d-c)\] done clear
  D)
  \[d-c\] done clear
  View Solution play_arrow

• question_answer93)
  If the sum of three numbers of a arithmetic sequence is 15 and the sum of their squares is 83, then the numbers are  [MP PET 1985]
  A)
  4, 5, 6 done clear
  B)
  3, 5, 7 done clear
  C)
  1, 5, 9 done clear
  D)
  2, 5, 8 done clear
  View Solution play_arrow

• question_answer94)
  The four arithmetic means between 3 and 23  are  [MP PET 1985]
  A)
  5, 9, 11, 13 done clear
  B)
  7, 11, 15, 19 done clear
  C)
  5, 11, 15, 22 done clear
  D)
  7, 15, 19, 21 done clear
  View Solution play_arrow

• question_answer95)
  If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are [MP PET 1986]
  A)
  21, 17, 13 done clear
  B)
  20,16, 12 done clear
  C)
  22, 18, 14 done clear
  D)
  24, 20, 16 done clear
  View Solution play_arrow

• question_answer96)
  If \[\frac{1}{p+q},\ \frac{1}{r+p},\ \frac{1}{q+r}\] are in A.P., then [RPET 1995]
  A)
  \[p,\ ,q,\ r\] are in A.P. done clear
  B)
  \[{{p}^{2}},\ {{q}^{2}},\ {{r}^{2}}\] are in A.P. done clear
  C)
  \[\frac{1}{p},\ \frac{1}{q},\ \frac{1}{r}\] are in A.P. done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer97)
  If \[1,\ {{\log }_{y}}x,\ {{\log }_{z}}y,\ -15{{\log }_{x}}z\] are in A.P., then
  A)
  \[{{z}^{3}}=x\] done clear
  B)
  \[x={{y}^{-1}}\] done clear
  C)
  \[{{z}^{-3}}=y\] done clear
  D)
  \[x={{y}^{-1}}={{z}^{3}}\] done clear
  E)
  All the above done clear
  View Solution play_arrow

• question_answer98)
  The difference between an integer and its cube is divisible by [MP PET 1999]
  A)
  4 done clear
  B)
  6 done clear
  C)
  9 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer99)
  If \[a,\,b,\,c\] are in A.P., then \[(a+2b-c)\]\[(2b+c-a)\]\[(c+a-b)\]  equals [Pb. CET 1999]
  A)
  \[\frac{1}{2}abc\] done clear
  B)
  abc done clear
  C)
  2 abc done clear
  D)
  4 abc done clear
  View Solution play_arrow

• question_answer100)
  Four numbers are in arithmetic progression. The sum of first and last term is 8 and the product of both middle terms is 15. The least number of the series is    [MP PET 2001]
  A)
  4 done clear
  B)
  3 done clear
  C)
  2 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer101)
  If twice the 11th term of an A.P. is equal to 7 times of its 21st term, then its 25th term is equal to [J & K 2005]
  A)
  24 done clear
  B)
  120 done clear
  C)
  0 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer102)
  If \[x,y,z\] are in A.P. and \[{{\tan }^{-1}}x,{{\tan }^{-1}}y\]and \[{{\tan }^{-1}}z\] are also in A.P., then [Kerala (Engg.) 2005]
  A)
  \[x=y=z\] done clear
  B)
  \[x=y=-z\] done clear
  C)
  \[x=1;y=2;z=3\] done clear
  D)
  \[x=2;y=4;z=6\] done clear
  E)
  \[x=2y=3z\] done clear
  View Solution play_arrow