The sum of the first $20$ terms common between the series $3 + 7 + 11 + 15 + \dots$ and $1 + 6 + 11 + 16 + \dots$ is

If the first term and the last term of an arithmetic progression are $a$ and $\ell$ respectively,and the sum of all its terms is $S$,then what is its common difference $d$?

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1 + (a_5 + a_{10} + a_{15} + \ldots + a_{2020}) + a_{2024} = 2233$. Then $a_1 + a_2 + a_3 + \ldots + a_{2024}$ is equal to . . . . . .

If the roots of the equation $x^3+3px^2+3qx-8=0$ are in an arithmetic progression,then $2p^3-3pq=$

The sum of the first four terms of an arithmetic progression is $56$. The sum of the last four terms is $112$. If its first term is $11$,then the number of terms is:

Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let $A_{k}=a_1^2-a_2^2+a_3^2-a_4^2+\ldots+a_{2k-1}^2-a_{2k}^2$. If $A_3=-153$,$A_5=-435$ and $a_1^2+a_2^2+a_3^2=66$,then $a_{17}-A_7$ is equal to: