The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\frac {27}{19}$. Then the common ratio of this series is

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 difference between the fourth term and the first term of a Geometrical Progresssion is $52.$ If the sum of its first three terms is $26,$ then the sum of the first six terms of the progression is

If $a _{1}(>0), a _{2}, a _{3}, a _{4}, a _{5}$ are in a G.P., $a _{2}+ a _{4}=2 a _{3}+1$ and $3 a _{2}+ a _{3}=2 a _{4}$, then $a _{2}+ a _{4}+2 a _{5}$ is equal to

Find the sum to $n$ terms of the sequence, $8,88,888,8888 \ldots$

Let $\mathrm{a}$ and $\mathrm{b}$ be be two distinct positive real numbers. Let $11^{\text {th }}$ term of a $GP$, whose first term is $a$ and third term is $b$, is equal to $p^{\text {th }}$ term of another $GP$, whose first term is $a$ and fifth term is $b$. Then $\mathrm{p}$ is equal to