The sum of the first $n$ terms of the $A.P.$ $-2, 1, 4, 7, \ldots$ is:

If the sum of the first $n$ terms of an $AP$ is $4n - n^2$,what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly,find the $3^{rd}$,the $10^{th}$ and the $n^{th}$ terms.

If $S_{n}$ denotes the sum of the first $n$ terms of an $AP$,prove that $S_{12} = 3(S_{8} - S_{4})$.

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

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

Find the sum of all the $11$ terms of an $AP$ whose middle most term is $30$.