Write the seventh term of the following $GP$: $6, 12, 24, 48, \ldots$

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

The $4$th term of an $A.P.$ is equal to $3$ times the first term and the seventh term exceeds twice the third term by $1$. Find the first term and the common difference.

Find the sum of infinite terms of the series $1+\frac{2}{3}+\frac{3}{3^{2}}+\frac{4}{3^{3}}+\frac{5}{3^{4}}+\cdots$

Let $G$ be the geometric mean of two positive numbers $a$ and $b,$ and $M$ be the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}.$ If $\frac{1}{M}:G$ is $4:5,$ then $a:b$ can be

The sum of an infinite geometric series is $3$. $A$ series,which is formed by squares of its terms,has the sum also $3$. The first series is