Find the sum of the following $APs$ $2, 7, 12, \ldots$ to $10$ terms.

Find the $20^{th}$ term from the last term of the $AP : 3, 8, 13, \ldots, 253.$

$A$ manufacturer of $TV$ sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year,find the production in the $1^{st}$ year.

$A$ manufacturer of $TV$ sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year,find the total production in first $7$ years.

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.

Are $a, a^{2}, a^{3}, a^{4}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.