Consider an infinite $G.P. $ with first term a and common ratio $r$, its sum is $4$ and the second term is $3/4$, then
$a = \frac{7}{4},\,r = \frac{3}{7}$
$a = \frac{3}{2},\,r = \frac{1}{2}$
$a = 2,\,r = \frac{3}{8}$
$a = 3,\,r = \frac{1}{4}$
The sum of some terms of $G.P.$ is $315$ whose first term and the common ratio are $5$ and $2,$ respectively. Find the last term and the number of terms.
The sum of infinite terms of a $G.P.$ is $x$ and on squaring the each term of it, the sum will be $y$, then the common ratio of this series is
If the ${4^{th}},\;{7^{th}}$ and ${10^{th}}$ terms of a $G.P.$ be $a,\;b,\;c$ respectively, then the relation between $a,\;b,\;c$ is
The sum of infinite terms of the geometric progression $\frac{{\sqrt 2 + 1}}{{\sqrt 2 - 1}},\frac{1}{{2 - \sqrt 2 }},\frac{1}{2}.....$ 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