SERIES
Category : 6th Class
Learning Objective
A series is a sequence of numbers/alphabetical letters or both which follow a particular rule. Each element of series is called 'term'. We have to analyse the pattern and find the missing term or next term to continue the pattern.
Types of Series are explained in the following chart:
In number series, relationship between the terms is of any kind. For example.
(a) Consecutive even numbers
(b) Consecutive odd numbers
(c) Consecutive prime numbers
(d) Square of numbers
(e) Cubes of numbers
(f) Square root of numbers
(g) Omission of certain number of letter in any consecutive order
(h) Addition/subtraction/multiplication/ division by some number (For Ex. A.P & G.P) or any other relation.
TYPES OF QUESTIONS:
(I) Complete the series
(II) Find missing number of the series
(III) Find wrong number of the series
EXAMPLES ON NUMBER SERIES
(I) COMPLETE THE SERIES
Example 1: 4, 6, 9, 13,....
(a) 17 (b) 18
(c) 19 (d) 20
Sol. (b)
[Correct answer
Example 2: 64, 32, 16, 8, ?
(a) 0 (b) 1
(c) 2 (d) 4
Sol. (d) Each number is half of its previous number.
Example 3: 4, 9, 16, 25,...
(a) 32 (b) 42
(c) 55 (d) 36
Sol. (d) Each number is a whole square.
Example 4: 2, 6, 12, 20, 30, 42, 56, ...
(a) 60 (b) 64
(c) 70 (d) 72
Sol. (d) 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8, 8 x 9 = 72
(II) TO FIND THE MISSING NUMBER OF SERIES:
Examples: 79, 87, ?, 89, 83
(a) 80, (b) 81
(c) 82 (d) 88
Sol. (b) 
Example 6: 37, 41, ?, 47, 53
(a) 42 (b) 43
(c) 46 (d) 44
Sol. (b) Consecutive prime numbers.
Example 7 : 21, 34, ?, 89, 144
(a) 43 (b) 55
(c) 64 (d) 71
Sol. (b) Each number is the sum of the two preceding numbers.
21 + 34 = 55
34 + 55 = 89
55 + 89 = 144
(III) TO FIND THE WRONG TERM IN THE SERIES:
EXAMPLES ON ALPHABETIC SERIES:
Example 8: Find the wrong term in the following series EG, JL, OQ, TW,..........
(a) EG (b) JL
(c) OQ (d) TW
Sol. (c) 
Example 9: G, H, J, M, ?
(a) R (b) S
(c) Q (d) P
Sol. (c) 
Example 10: BF, CH, ? , HO, LT
(a) EG (b) EK
(c) CE (d) FJ
Sol. (b) 
Example 11: DCXW, FEW, HGTS, ?
(a) LKPO (b) ABYZ
(c) JIRQ (d) LMRS
Sol. (c) JIRQ
EXAMPLES ON ALPHA-NUMERIC SERIES
Example 12: K 1, M 3, P 5, T 7, ?
(a) Y 9 (b) Y 11
(c) V 9 (d) v 11
Sol. (b) Alphabets follow the sequence
And numbers are increasing by 2
Example 13: Find the missing term.
2 Z 5, 7 Y 7, 14 X 9, 23 W 11, 34 V 13, ?
Sol. First number is the sum of the number of the proceeding term.
Middle letter is moving one step backward.
Third number in a term is a series of odd numbers.
\[\therefore \] 6th term = 47 U 15.
EXAMPLES ON MIXED SERIES
Example 14: Complete the series Z, L, X, J, V, H, T, F, _, _
(a) D, R (b) R, D
(c) D, D (d) R, R
Sol. (b) The given sequence consists of two series
(i) Z, X, V, T, _
(ii) L, J, H, F, _. Both consisting of alternate letters in the reverse order.
Next term of (i) series = R, and
Next term of (ii) series = D
Example 15: 7, 5, 26, 17, 63, 37, 124, 65,?,?
(a) 101, 215 (b) 101,101
(c) 215, 101 (d) 215, 215
Sol. (c) The given series consists of two series
(i) 7, 26, 63, 124.....
(ii) 5, 17, 37, 65.....
In the first series,
\[7={{2}^{3}}\,-1,\,\,26\,={{3}^{3}}-1,\,63={{4}^{3}}-1\]
\[124={{5}^{3}}-1,\,\,\therefore \,{{6}^{3}}-1=215\]
and in the second series.
\[5={{2}^{2}}+1,\,\,17={{4}^{2}}+1,\]
\[37={{6}^{2}}+1,\,65={{8}^{2}}+1\]
\[\therefore \,\,\,\,{{10}^{2}}+1=101\]
EXAMPLES ON LETTER SERIJS
Example 16: b a a b – a b a – b b a - -
(a) bbaa (b) aaaa
(c) abab (d) baba
Sol. (d) \[b\,a\,a\,b\,\underline{b}\,a\,/\,b\,a\,\underline{a}\,b\,b\,a\,/\,\underline{b}\,\underline{a}\].
Example 17: - - a a b – a – a – b a
(a) bbaab (b) ababa
(c) bbabb (d) aaaba
Sol. (b) aba/aba/aba/aba.
EXAMPLES ON CORRESPONDENCE SERIES
Example 18: A_ BAC_D_BCDC
_ 3 _ 2 _ 1 _ 4 ? ? ? ?
d c _ _ b a c b _ _ _ _
(a) 1, 3, 4, 3 (b) 1, 4, 3, 4
(c) 2, 3, 4, 3 (d) 3, 4, 1, 4
Sol. (b) Clearly, 2 corresponds to A.
Now, b corresponds to C and 4 corresponds to b. So, 4 corresponds to C.
c corresponds to D and 3 corresponds to c. So, 3 corresponds to D.
so, the remaining number i.e., 1 corresponds to B.
Thus, BCDC corresponds to 1, 4, 3, 4.
Example 19: C B _ _ D _ B A B C C B
_ _ 1 2 4 3 _ _ ? ? ? ?
a _ a b _ c _ b _ _ _ _
(a) 3, 4, 4, 3 (b) 3, 2, 2, 3
(c) 3, 1, 1, 3 (d) 1, 4, 4, 1
Sol. Comparing the positions of the capital letters, numbers and small letters, we find:
a responds to C and 1 corresponds to a. So, a and 1 correspond to C.
b corresponds to A and 2 corresponds to b. So, b and 2 correspond to A.
Also, 4 corresponds to D.
Sa, the remaining number i.e. 3 corresponds to B. So, BCCB corresponds to 3, 1, 1, 3.
You need to login to perform this action.
You will be redirected in
3 sec
