Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{20} = 790$ and $S_{10} = 145$,then $S_{15} - S_5$ is:

The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$,then find the number of terms.

The ratio of the sum of $m$ and $n$ terms of an $A.P.$ is $m^2:n^2$. Then the ratio of the $m^{th}$ and $n^{th}$ term will be:

What is the sum of all numbers between $100$ and $300$ that are divisible by $7$?

The first term of an arithmetic progression is $10$ and the last term is $50$. If the sum of all its terms is $300$,then the number of terms $n = ...$

Four numbers are in arithmetic progression. The sum of the first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is