If $a, b, c$ are in Arithmetic Progression,then $(a + 2b - c)(2b + c - a)(a + 2b + c) = \dots$

If $S_n$ denotes the sum of $n$ terms of an arithmetic progression,then the value of $(S_{2n} - S_n)$ is equal to

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 the sequence $a_{n}$ be defined as follows:
$a_{1} = 1, a_{n} = a_{n-1} + 2$ for $n \ge 2$
Find the first five terms and write the corresponding series.

If the sum of $n$ terms of an $A.P.$ is $3n^2 + 5n$ and $T_m = 164$,then $m = $

$150$ workers were engaged to finish a job in a certain number of days. $4$ workers dropped out on the second day,$4$ more workers dropped out on the third day,and so on. It took $8$ more days to finish the work. Find the number of days in which the work was completed.