Find the sum of the following $APs$ $-37, -33, -29, \ldots$ to $12$ terms.

Are $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write the next three terms.

$A$ contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ $200$ for the first day,₹ $250$ for the second day,₹ $300$ for the third day,etc. The penalty for each succeeding day is ₹ $50$ more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by $30$ days?

How many terms of the $AP : 9, 17, 25, \ldots$ must be taken to give a sum of $636$?

In an $AP$ given $a=3, n=8, S_n=192,$ find $d$.

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = 10, d = 10.$