If the sum of first $n$ terms of an $A.P.$ is $c n^2$, then the sum of squares of these $n$ terms is
$\frac{n\left(4 n^2-1\right) c^2}{6}$
$\frac{n\left(4 n^2+1\right) c^2}{3}$
$\frac{n\left(4 n^2-1\right) c^2}{3}$
$\frac{n\left(4 n^2+1\right) c^2}{6}$
If $f(x + y,x - y) = xy\,,$ then the arithmetic mean of $f(x,y)$ and $f(y,x)$ is
Which of the following sequence is an arithmetic sequence
If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and product of remaining two middle term is $15$, then greatest number of the series will be
If all interior angle of quadrilateral are in $A.P.$ If common difference is $10^o$, then find smallest angle ? .............. $^o$
Let ${\left( {1 - 2x + 3{x^2}} \right)^{10x}} = {a_0} + {a_1}x + {a_2}{x^2} + .....+{a_n}{x^n},{a_n} \ne 0$, then the arithmetic mean of $a_0,a_1,a_2,...a_n$ is