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

$A$ 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.

Find the sum of the first $22$ terms of the $AP : 8, 3, -2, \ldots$

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a=4, d=-3.$

Show that $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ form an $AP$ where $a_{n}$ is defined as $a_{n}=9-5n$. Find the sum of the first $15$ terms.

Check whether $301$ is a term of the list of numbers $5, 11, 17, 23, \ldots$