For a given $A.P.$,the first term is $5$ and the common difference is $12$. Find the $25^{th}$ term of the $A.P.$

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.

For the $A.P.$ $3, 13, 23, 33, \ldots,$ its $\ldots \ldots \ldots \ldots$ term exceeds its $21^{st}$ term by $10.$

Which term of the $A.P.$ $5, 15, 25, \ldots$ exceeds its $31^{st}$ term by $130$ (in $^{th}$)?

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

For each of the following $A.P.s$,find the $n^{th}$ term: $\frac{4}{3}, 2, \frac{8}{3}, \frac{10}{3}, \ldots$