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

From natural numbers $1$ to $288,$ find the number $x$ such that the sum of all natural numbers smaller than $x$ is equal to the sum of all natural numbers greater than $x$ but less than or equal to $288.$

The sum of the first $n$ terms of the $A.P.$ $2, 7, 12, 17, \ldots$ is $990$. Find the value of $n$.

For an $A.P.$,$T_{n} = \ldots \ldots \ldots \ldots (n > 1)$

The number of terms in the finite $A.P.$ $13, 26, 39, \ldots, 650$ is ........

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = \frac{15}{2}, \quad d = \frac{3}{2}$