Let $a_n, n \geq 1$, be an arithmetic progression with first term $2$ and common difference $4$ . Let $M_n$ be the average of the first $n$ terms. Then the sum $\sum \limits_{n=1}^{10} M_n$ is

If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then

In $\Delta ABC$, if $a, b, c$ are in $A.P.$ (with usual notations), identify the incorrect statements -

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is

Write the first five terms of the following sequence and obtain the corresponding series :

$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$

The sum of all those terms, of the anithmetic progression $3,8,13, \ldots \ldots .373$, which are not divisible by $3$,is equal to $.......$.