$8^{th}$ term of the series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ will be (in $\sqrt{2}$)

If the $5^{th}$ term of a $G.P.$ is $\frac{1}{3}$ and $9^{th}$ term is $\frac{16}{243}$,then the $4^{th}$ term will be

Let $a, b$ and $c$ be in $G.P.$ with common ratio $r,$ where $a \ne 0$ and $0 < r \le \frac{1}{2}.$ If $3a, 7b$ and $15c$ are the first three terms of an $A.P.,$ then the $4^{th}$ term of this $A.P.$ is

The arithmetic mean of the first $n$ natural numbers is:

The sum of the first two terms of a $G.P.$ is $36$ and the product of the first and the third terms is $9$ times the second term,then find the sum of the first $8$ terms.

In a geometric progression,if the ratio of the sum of first $5$ terms to the sum of their reciprocals is $49$,and the sum of the first and the third term is $35$. Then the first term of this geometric progression is