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

$A$ 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?

In an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.

In an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.

Determine the $AP$ whose third term is $16$ and the $7^{th}$ term exceeds the $5^{th}$ term by $12$.

Find the $31^{st}$ term of an $AP$ whose $11^{th}$ term is $38$ and the $16^{th}$ term is $73.$