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

Let $S_{n}$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 530$ and $S_{5} = 140$,then $S_{20} - S_{6}$ is equal to:

Show that the sum of $(m+n)^{th}$ and $(m-n)^{th}$ terms of an $A.P.$ is equal to twice the $m^{th}$ term.

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day,$4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is

Find the sum of integers from $1$ to $100$ that are divisible by $2$ or $5.$