The arithmetic mean of the first $n$ even natural numbers is ..........

The sum of all integers between $1$ and $100$ (both inclusive) which are divisible by $5$ or $13$ is

The first term of an $A.P.$ is $2$ and the common difference is $4$. The sum of its $40$ terms will be:

If $a, b, c$ are in $A.P.$,then $(a + 2b - c)(2b + c - a)(c + a - b)$ equals

Suppose that the number of terms in an $A.P.$ is $2k$,where $k \in N$. If the sum of all odd-positioned terms of the $A.P.$ is $40$,the sum of all even-positioned terms is $55$,and the last term of the $A.P.$ exceeds the first term by $27$,then $k$ is equal to:

Four numbers are in an arithmetic progression. The sum of the first and last terms is $8$ and the product of the two middle terms is $15$. What is the smallest number in the sequence?