Question

If in a geometric progression $\left\{ a _ { n } \right\} , a _ { 1 } = 3 , a _ { n } = 96$ and $S _ { n } = 189$ then the value of $n$ is.

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (B)

6

Answer 2

$a _ { 1 } = 3 , a _ { n } = 96$ $\Rightarrow$ $a _ { 1 } r ^ { n - 1 } = 96$ $\Rightarrow$ $r ^ { n - 1 } = 32$ …..(i)

$S _ { n } = \frac { a _ { 1 } \left( r ^ { n } - 1 \right) } { r - 1 } = 189$ $\Rightarrow$ $\frac { 3 ( 32 r - 1 ) } { r - 1 } = 189$

Hence $r = 2$ and $n = 6$.