Sequence And Series Question 135
Question: If in a geometric progression $ { a_{n} },\ a_1=3,\ a_{n}=96 $ and $ S_{n}=189 $ then the value of $ n $ is
Options:
A) 5
B) 6
C) 7
D) 8
Show Answer
Answer:
Correct Answer: B
Solution:
$ a_1=3,\ a_{n}=96 $
$ \Rightarrow $ $ a_1{r^{n-1}}=96 $
$ \Rightarrow $ $ {r^{n-1}}=32 $ ?..(i) $ S_{n}=\frac{a_1(r^{n}-1)}{r-1}=189 $
$ \Rightarrow $ $ \frac{3(32r-1)}{r-1}=189 $ Hence $ r=2 $ and $ n=6 $ .
BETA
