Sequence And Series Question 57
Question: If the sum of first 6 term is 9 times to the sum of first 3 terms of the same G.P., then the common ratio of the series will be
[RPET 1985]
Options:
A) $ -2 $
B) 2
C) 1
D) 1/2
Show Answer
Answer:
Correct Answer: B
Solution:
Under given conditions, we get
$ \Rightarrow $ $ \frac{a(r^{6}-1)}{(r-1)}=9.\frac{a(r^{3}-1)}{(r-1)} $ $ (\because \ r>1) $
$ \Rightarrow $ $ r^{6}-1=9r^{3}-9 $
$ \Rightarrow $ $ {{(r^{3})}^{2}}-9(r^{3})+8=0 $
$ \Rightarrow $ $ (r^{3}-1)(r^{3}-8)=0 $
$ \Rightarrow $ $ r=1,\ \omega ,\ {{\omega }^{2}} $ and $ r=2 $ . But $ r=1,\ \omega ,\ {{\omega }^{2}} $ cannot satisfy the given condition. Hence $ r=2 $ .
BETA
