A) Only (a)
B) Only (b)
C) Both (a) and (b)
D) (a), (b) and (c)
Correct Answer: D
Solution :
(a) Given A.P. is \[\sqrt{2},\,2\sqrt{2},\,3\sqrt{2},\,4\sqrt{2},......\] \[{{S}_{n}}=\frac{n}{2}\left[ 2\left( \sqrt{2} \right)+\left( n-1 \right)\,\left( \sqrt{2} \right) \right]\] \[=\frac{n}{2}\times \sqrt{2}\left[ 2+n-1 \right]=\frac{n}{\sqrt{2}}\left[ n+1 \right]\] (b) Since, \[{{a}_{n}}=3n+2\] Here, \[{{a}_{1}}=3(1)+2=5\] \[{{a}_{2}}=3(2)+2=8\] \[\therefore \] Common difference \[={{a}_{2}}-{{a}_{1}}=3\] (c) Given A.P. is \[\left( -5 \right),\,\left( -8 \right),\,\left( -11 \right),......(-230)\] \[\because \] \[{{a}_{n}}=a+(n-1)\,(-3)\] \[\Rightarrow \] \[-230=-5+(n-1)\,(-3)\] \[\Rightarrow \] \[\frac{-225}{-3}=(n-1)\Rightarrow n=75+1=76\] \[\Rightarrow \] \[{{S}_{n}}=\frac{76}{2}\left( \left( -5 \right)+\left( -230 \right) \right)=-8930\]
You need to login to perform this action.
You will be redirected in
3 sec
