If the $n^{th}$ term of an arithmetic progression is $3n - 1$,then the sum of its first five terms is.......

If the $A.M.$ between $p^{th}$ and $q^{th}$ terms of an $A.P.$ is equal to the $A.M.$ between $r^{th}$ and $s^{th}$ terms of the same $A.P.$,then $p + q$ is equal to

Suppose that all the terms of an arithmetic progression $(A.P.)$ are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6:11$ and the seventh term lies between $130$ and $140$,then the common difference of this $A.P.$ is

If $a$ and $b$ are two numbers,$A$ is the arithmetic mean,and $S$ is the sum of $n$ arithmetic means between $a$ and $b$,then what does $S/A$ depend on?

If $a + 2b + 3c = 6$,then the greatest value of $abc^2$ is (where $a, b, c$ are positive real numbers).

Six numbers are in an $AP$ such that their sum is $3$. The first term is $4$ times the third term. Then, the fifth term is: