If $a_1, a_2, a_3, \dots$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$,then the sum of the first $15$ terms of this $A.P.$ is

Let there be four distinct integers in an increasing arithmetic progression. One of these integers is equal to the sum of the squares of the other three. What is the product of all these numbers?

The sum of the series $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + \dots$ to $9$ 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:

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is

The sum of $n$ arithmetic means between $a$ and $b$ is: