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

For an $A.P.$,the first term is $10$,the $n^{th}$ term is $40$,and the sum of the first $n$ terms is $150$. Find the value of $n$ and the common difference $d$.

The $7^{th}$ term of an $A.P.$ is $108$ and the $11^{th}$ term is $212$. Then,its $n^{th}$ term is $\ldots \ldots \ldots \ldots$

The ratio of the sums of first $n$ terms of two $A.P.s$ is $(5n - 3) : (7n + 2)$. Find the ratio of their $m^{th}$ terms.

If $2x$,$x+10$,and $3x+2$ are three consecutive terms of an $A.P.$,find the value of $x$.

Verify that each of the following is an $AP$,and then write its next three terms.
$\sqrt{3}, 2 \sqrt{3}, 3 \sqrt{3}, \ldots$