The $7^{th}$ term of an $A.P.$ is $108$ and the $11^{th}$ term is $212$. Then,its $n^{th}$ term is $\ldots \ldots \ldots \ldots$

Find the sum of the first seven numbers which are multiples of $2$ as well as of $9$.

If $a=2$ and $d=4,$ then $S_{40}=\ldots \ldots \ldots$

Let $S_n$,$S_{2n}$,and $S_{3n}$ be the sums of $n$,$2n$,and $3n$ terms of an Arithmetic Progression $(AP)$,respectively. Prove that $S_{3n} = 3(S_{2n} - S_n)$.

The $10^{th}$ term of an $A.P.$ is $52$ and its $17^{th}$ term exceeds its $13^{th}$ term by $20$. Find the $A.P.$ and also its $30^{th}$ term.

How many terms of the $A.P.$ $8, 15, 22, \ldots$ add up to $1490$?