If the first term of a $G.P.$ be $5$ and common ratio be $ - 5$, then which term is $3125$
${6^{th}}$
${5^{th}}$
${7^{th}}$
${8^{th}}$
If the first and the $n^{\text {th }}$ term of a $G.P.$ are $a$ and $b$, respectively, and if $P$ is the product of $n$ terms, prove that $P^{2}=(a b)^{n}$
Given $a_1,a_2,a_3.....$ form an increasing geometric progression with common ratio $r$ such that $log_8a_1 + log_8a_2 +.....+ log_8a_{12} = 2014,$ then the number of ordered pairs of integers $(a_1, r)$ is equal to
The sum of the series $5.05 + 1.212 + 0.29088 + ...\,\infty $ is
The sum of the series $3 + 33 + 333 + ... + n$ terms 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