In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = 21, d = -7$.

(A) The general form of an $A.P.$ is given by $a, a+d, a+2d, a+3d, \ldots$
Given $a = 21$ and $d = -7$.
First term $T_1 = a = 21$.
Second term $T_2 = a + d = 21 + (-7) = 14$.
Third term $T_3 = a + 2d = 21 + 2(-7) = 21 - 14 = 7$.
Fourth term $T_4 = a + 3d = 21 + 3(-7) = 21 - 21 = 0$.
Thus,the $A.P.$ is $21, 14, 7, 0, \ldots$
The general term $T_n$ is given by $T_n = a + (n-1)d = 21 + (n-1)(-7) = 21 - 7n + 7 = -7n + 28$.