The $9^{th}$ term of the sequence $0, 3, 8, 15, 24, 35, \dots$ is

If $S_n = 1 + \frac{1}{2} + \frac{1}{2^2} + \dots + \frac{1}{2^{n-1}}$,then the least integral value of $n$ such that $2 - S_n < \frac{1}{100}$ is

Let $f: R \rightarrow R$ be such that for all $x \in R$,$(2^{1+x}+2^{1-x})$,$f(x)$,and $(3^x+3^{-x})$ are in $A.P.$. Then,the minimum value of $f(x)$ is:

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

$a, g, h$ are the arithmetic mean,geometric mean,and harmonic mean between two positive numbers $x$ and $y$ respectively. Identify the correct statement among the following:

The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is