If $\frac{1}{p + q}, \frac{1}{r + p}, \frac{1}{q + r}$ are in $A.P.$,then

Let $S_{1}$ be the sum of the first $2n$ terms of an arithmetic progression. Let $S_{2}$ be the sum of the first $4n$ terms of the same arithmetic progression. If $(S_{2} - S_{1})$ is $1000$,then the sum of the first $6n$ terms of the arithmetic progression is equal to:

If the sum of $n$ terms of an $A$.$P$. is $3n^2 + 5n$ and its $m$th term is $164$, then the value of $m$ is

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

The sum of the first and third term of an arithmetic progression is $12$ and the product of the first and second term is $24$. Find the first term.

Find the sum of all natural numbers lying between $100$ and $1000$ which are multiples of $5.$