If the $p^{th}$ term of an AP is $q \& q^{th}$ term is $p$, then prove that its $n^{th}$ term is $\left(p+q-n\right)$.

If $p^{th}, q^{th} \& r^{th}$ terms of an AP are $a, b \& c$ respectively, then show that $a\left(q-r\right)+b\left(r-p\right)+c\left(p-q\right)=0$.

If the $n^{th}$ term of the two APs $9, 7, 5, .... \& 24, 21, 18,...$ are the same, find the value of $n$. Also find that term.

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

How many two-digit numbers are divisible by $7$?

How many natural numbers are there between $200 \& 500$ which are divisible by $7$.

Find the number of natural numbers between $101$ and $999$ which are divisible by both $2 \& 5$.

How many numbers lies between $10 \&\hspace{0.17em}300$, which when divided by $4$ leave a remainder $3$?

How many three-digit numbers are divisible by $12?$