Sequence And Series Question 459
Question: In a, GP. of 3n terms, $ S_1 $ denotes the sum of first n terms, $ S_2 $ the sum of the second block of n terms and $ S_3 $ the sum of last n terms. Then $ S_1,S_2,S_3, $ are in
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let the 3n terms of GP. be $ a,ar,ar^{2},…..a{r^{n-1}},ar^{n},a{r^{n+1}},…a{r^{2n-1}},ar^{2n},a{r^{2n+1}},….., $ $ a{r^{3n-1}} $ . Then $ S_1=a+ar+ar^{2}+……+a{r^{n-1}}=\frac{a(1-r^{n})}{1-r} $ $ S_2=ar^{n}+a{r^{n+1}}+…..+a{r^{2n-1}}=\frac{ar^{n}(1-r^{n})}{1-r} $ $ S_3=ar^{2n}+a{r^{2n+1}}+…..+a{r^{3n-1}}=\frac{ar^{2n}(1-r^{n})}{1-r} $ Clearly $ \frac{S_2}{S_1}=\frac{S_3}{S_2}=r^{n} $
BETA
