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

Find the $m^{\mathrm{th}}$ term of an Arithmetic progression whose ${12}^{\mathrm{th}}$ term exceeds the $5^{\mathrm{th}}$ term by $14$ and the sum of both terms is $36$.

Which term of the arithmetic progression $3, 15, 27, 39, .....$ will be $132$ more than its ${54}^{\mathrm{th}}$ term?

The sum of the $4^{\mathrm{th}}$ and $8^{\mathrm{th}}$ terms of an arithmetic progression is $24$ and the sum of the $6^{\mathrm{th}}$ and ${10}^{\mathrm{th}}$ terms is $44$. Find the first three terms of the arithmetic progression.

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

If in an arithmetic progression $p^{\mathrm{th}}$ term is $\frac{1}{q}$ and $q^{\mathrm{th}}$ term is $\frac{1}{p}$, then prove that $(pq{)}^{\mathrm{th}}$ term of arithmetic progression is $1$.

If $p^{\mathrm{th}}$ term is $q$ and $q^{\mathrm{th}}$ term is $p$ of an arithmetic progression, then prove that $(p+q{)}^{\mathrm{th}}$ term is $0$.

$p^{\mathrm{th}}$, $q^{\mathrm{th}}$ and $r^{\mathrm{th}}$ terms of an arithmetic progression are $a, b, c$ respectively then prove that $a(q-r)+b(r-p)+c(p-q)=0$