In an $AP$ given $a_{12}=37$ and $d=3$,find the first term $a$ and the sum of the first $12$ terms $S_{12}$.

Find the sum of the first $51$ terms of an $AP$ whose second and third terms are $14$ and $18$ respectively.

Find the sum given below: $-5 + (-8) + (-11) + \ldots + (-230)$

Find the sum of the first $40$ positive integers divisible by $6$.

$A$ 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.

$-10, -6, -2, 2, \ldots$ are $APs$? If they form an $AP$,find the common difference $d$ and write three more terms.