Find the sum of the first $30$ terms of the $A.P.$ $15, 20, 25, \ldots$

What is the common difference of an $AP$ in which $a_{18}-a_{14}=32$?

The ratio of the $11^{\text{th}}$ term to the $18^{\text{th}}$ term of an $AP$ is $2:3$. Find the ratio of the $5^{\text{th}}$ term to the $21^{\text{st}}$ term,and also the ratio of the sum of the first five terms to the sum of the first $21$ terms.

Justify whether it is true to say that the following are the $n^{\text{th}}$ terms of an $AP.$
$(i)$ $2n-3$
$(ii)$ $3n^{2}+5$
$(iii)$ $1+n+n^{2}$

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $5, 11, 17, 23, \ldots$

Find the sum of the first seven numbers which are multiples of $2$ as well as of $9$.