If the sum of three terms of $G.P.$ is $19$ and product is $216$, then the common ratio of the series is
$ - \frac{3}{2}$
$\frac{3}{2}$
$2$
$3$
If ${(p + q)^{th}}$ term of a $G.P.$ be $m$ and ${(p - q)^{th}}$ term be $n$, then the ${p^{th}}$ term will be
Find the $12^{\text {th }}$ term of a $G.P.$ whose $8^{\text {th }}$ term is $192$ and the common ratio is $2$
The $4^{\text {tht }}$ term of $GP$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$. Let $S_n$ denote the sum of the first $n$ terms of this GP. If $S_6 > S_5+1$ and $S_7 < S_6+\frac{1}{2}$, then the number of possible values of $m$ is $..........$
If the third term of a $G.P.$ is $4$ then the product of its first $5$ terms is
Let $b_1, b_2,......, b_n$ be a geometric sequence such that $b_1 + b_2 = 1$ and $\sum\limits_{k = 1}^\infty {{b_k} = 2} $ Given that $b_2 < 0$ , then the value of $b_1$ is