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

If the sum and product of the first three term in an $A.P$. are $33$ and $1155$, respectively, then a value of its $11^{th}$ tern is

Let the sum of $n, 2 n, 3 n$ terms of an $A.P.$ be $S_{1}, S_{2}$ and $S_{3},$ respectively, show that $S_{3}=3\left(S_{2}-S_{1}\right)$

If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =

Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-

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