The sum of the first two terms of a $G.P.$ is $1$ and every term of this series is twice its previous term. Then,the first term will be:

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,then $a^{q - r} b^{r - p} c^{p - q}$ is equal to

The product $(32)(32)^{1/6}(32)^{1/36} \dots \infty$ is

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$,will be

Let $a, b \in R$ be such that $a, a + 2b, 2a + b$ are in $A.P.$ and $(b + 1)^2, ab + 5, (a + 1)^2$ are in $G.P.$ then $(a + b)$ equals

When the $9^{th}$ term of an $A.P.$ is divided by its $2^{nd}$ term,the quotient is $5$. When the $13^{th}$ term is divided by the $6^{th}$ term,the quotient is $2$ and the remainder is $5$. Find the first term of the $A.P.$