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

In which of the following situations,does the list of numbers involved make an arithmetic progression,and why? The amount of money in the account every year,when ₹ $10000$ is deposited at compound interest at $8 \%$ per annum.

Show that $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ form an $AP$ where $a_{n}$ is defined as $a_{n}=3+4 n$. Also,find the sum of the first $15$ 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.

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

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