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

In an $AP$ given $a_{n}=4, d=2, S_{n}=-14$,find $n$ and $a$.

$A$ small terrace at a football ground comprises of $15$ steps each of which is $50 \, m$ long and built of solid concrete. Each step has a rise of $\frac{1}{4} \, m$ and a tread of $\frac{1}{2} \, m$. Calculate the total volume of concrete required to build the terrace (in $m^3$).

In an $AP$ given $a_{12}=37$ and $d=3$,find the first term $a$ and the sum of the first $12$ terms $S_{12}$.

$A$ sum of ₹ $1000$ is invested at $8 \%$ simple interest per year. Calculate the interest at the end of each year. Do these interests form an $AP$? If so,find the interest at the end of $30 \text{ years}$ making use of this fact. (in ₹)

How many two-digit numbers are divisible by $3$?