In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = -15, d = -7$.

(A) The general form of an $A.P.$ is given by $a, a+d, a+2d, a+3d, \ldots$
Given $a = -15$ and $d = -7$.
First term $a_1 = -15$.
Second term $a_2 = a + d = -15 + (-7) = -22$.
Third term $a_3 = a + 2d = -15 + 2(-7) = -15 - 14 = -29$.
Fourth term $a_4 = a + 3d = -15 + 3(-7) = -15 - 21 = -36$.
The $n^{th}$ term is given by $T_n = a + (n-1)d = -15 + (n-1)(-7) = -15 - 7n + 7 = -7n - 8$.
Thus,the $A.P.$ is $-15, -22, -29, -36, \ldots$ and the general term is $T_n = -7n - 8$.