If $2x$,$x+10$,and $3x+2$ are three consecutive terms of an $A.P.$,find the value of $x$.

Which term of the $A.P.$ $53, 48, 43, \ldots$ is its first negative term? Find that term.

For a given finite $A.P.$,$a=2, n=8$ and $S_{8}=72$. Then,$l=........$

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 $S_{3n} = 3(S_{2n} - S_n)$.

For an $A.P.$,the $7^{th}$ term is $-1$ and the $16^{th}$ term is $17$. Find the general term of the $A.P.$

The sum of the first $n$ terms of an $A.P.$ is given by $S_n = 3n^2 + 5n$. Then,the $n^{th}$ term of the $A.P.$ $T_n = \ldots$