In an $AP$,given $a=8, a_{n}=62, S_{n}=210$,find $n$ and $d$.

In an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

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.

Which term of the $AP : 121, 117, 113, \ldots$ is its first negative term?

Do $1, -1, -3, -5, \ldots$ form an $AP$? If they form an $AP$,write the next two terms.

$A$ sum of ₹ $700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ $20$ less than its preceding prize,find the value of each of the prizes.