If the first term of an arithmetic progression is $2$ and the common difference is $4$,then the sum of its first $40$ terms is........

If the $9^{th}$ term of an $A.P.$ is $35$ and the $19^{th}$ term is $75$,then its $20^{th}$ term will be:

Let $x_n, y_n, z_n, w_n$ denote the $n^{th}$ terms of four different arithmetic progressions with positive terms. If $x_4 + y_4 + z_4 + w_4 = 8$ and $x_{10} + y_{10} + z_{10} + w_{10} = 20$,then the maximum value of $x_{20} \cdot y_{20} \cdot z_{20} \cdot w_{20}$ is:

If the sum of $n$ terms of an arithmetic progression is given by $Pn + Qn^2$,where $P$ and $Q$ are constants,what is the common difference?

If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.

The ratio of the sums of $m$ and $n$ terms of an $A.P.$ is $m^{2}: n^{2}$. Show that the ratio of the $m^{th}$ and $n^{th}$ term is $(2m-1):(2n-1)$.