Let $S_{1}$ be the sum of first $2 n$ terms of an arithmetic progression. Let, $S_{2}$ be the sum of first $4n$ terms of the same arithmetic progression. If $\left( S _{2}- S _{1}\right)$ is $1000,$ then the sum of the first $6 n$ terms of the arithmetic progression is equal to:
$1000$
$7000$
$5000$
$3000$
If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be
Let ${S_n}$ denotes the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$, then ratio $\frac{{{S_{3n}}}}{{{S_n}}} = $
If $a,b,c$ are in $A.P.$, then $\frac{1}{{\sqrt a + \sqrt b }},\,\frac{1}{{\sqrt a + \sqrt c }},$ $\frac{1}{{\sqrt b + \sqrt c }}$ are in
The arithmetic mean of first $n$ natural number
$8^{th}$ term of the series $2\sqrt 2 + \sqrt 2 + 0 + .....$ will be