For the $A.P.$ $-2, -4, -6, \ldots,$ the common difference $d = \ldots$

Find the sum of the first $25$ terms of the $A.P.$ $3, \frac{9}{2}, 6, \frac{15}{2}, \ldots$

The $7^{th}$ and $12^{th}$ terms of an $A.P.$ are $46$ and $71$ respectively. Find the $n^{th}$ term of the $A.P.$

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 5 - 6n$. Find the sum of the first $n$ terms of the $A.P.$

The first term of an $AP$ is $-5$ and the last term is $45$. If the sum of the terms of the $AP$ is $120$,then find the number of terms and the common difference.

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a=8, d=5$