The sum can be found of a infinite $G.P.$ whose common ratio is $r$
For all values of $r$
For only positive value of $r$
Only for $0 < r < 1$
Only for $ - 1 < r < 1(r \ne 0)$
Sum of infinite number of terms in $G.P.$ is $20$ and sum of their square is $100$. The common ratio of $G.P.$ is
Let $a$ and $b$ be roots of ${x^2} - 3x + p = 0$ and let $c$ and $d$ be the roots of ${x^2} - 12x + q = 0$, where $a,\;b,\;c,\;d$ form an increasing G.P. Then the ratio of $(q + p):(q - p)$ is equal to
Let $a _1, a _2, a _3, \ldots$ be a $G.P.$ of increasing positive numbers. Let the sum of its $6^{\text {th }}$ and $8^{\text {th }}$ terms be $2$ and the product of its $3^{\text {rd }}$ and $5^{\text {th }}$ terms be $\frac{1}{9}$. Then $6\left( a _2+\right.$ $\left.a_4\right)\left(a_4+a_6\right)$ is equal to
If the first term of a $G.P.$ be $5$ and common ratio be $ - 5$, then which term is $3125$