If the sum of first $n$ terms of an $A.P.$ is $cn(n -1)$ , where $c \neq 0$ , then sum of the squares of these terms is
$c^2n^2(n+1)^2$
$\frac{2}{3}c^2n(n-1)(2n-1)$
$\frac{2}{3}c^2n(n+1)(2n+1)$
$\frac{c^2 n^2}{3}(n+1)^2$
If $A$ be an arithmetic mean between two numbers and $S$ be the sum of $n$ arithmetic means between the same numbers, then
If the sum of the series $2 + 5 + 8 + 11............$ is $60100$, then the number of terms are
The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?
Let $a_{1}, a_{2} \ldots, a_{n}$ be a given $A.P.$ whose common difference is an integer and $S _{ n }= a _{1}+ a _{2}+\ldots+ a _{ n }$ If $a_{1}=1, a_{n}=300$ and $15 \leq n \leq 50,$ then the ordered pair $\left( S _{ n -4}, a _{ n -4}\right)$ is equal to
If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be