Let $a_1, a_2, ..., a_{10}$ be a $G.P.$ If $\frac{a_3}{a_1} = 25$,then $\frac{a_9}{a_5}$ is equal to:

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to

Let $a_{n}$ be the $n^{\text{th}}$ term of a $G$.$P$. of positive terms. If $\sum_{n=1}^{100} a_{2n+1} = 200$ and $\sum_{n=1}^{100} a_{2n} = 100$,then $\sum_{n=1}^{200} a_{n}$ is equal to:

The sum of the series $6 + 66 + 666 + \dots$ up to $n$ terms is:

Terms $a, 1, b$ are in arithmetic progression and terms $1, a, b$ are in geometric progression. Find $a$ and $b$ (given $a \neq b$).

Let $a_1, a_2, \dots, a_{10}$ be in $A.P.$ and $h_1, h_2, \dots, h_{10}$ be in $H.P.$ If $a_1 = h_1 = 2$ and $a_{10} = h_{10} = 3$,then $a_4 h_7$ is