In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a=8, d=5$
(A) The general form of an $A.P.$ is given by $a, a+d, a+2d, a+3d, \ldots$
Given $a = 8$ and $d = 5$.
Substituting these values:
First term $(T_1)$ = $a = 8$
Second term $(T_2)$ = $a + d = 8 + 5 = 13$
Third term $(T_3)$ = $a + 2d = 8 + 2(5) = 8 + 10 = 18$
Fourth term $(T_4)$ = $a + 3d = 8 + 3(5) = 8 + 15 = 23$
Thus,the $A.P.$ is $8, 13, 18, 23, \ldots$
The general term $T_n$ is given by $T_n = a + (n-1)d = 8 + (n-1)5 = 8 + 5n - 5 = 5n + 3$.
Given $a = 8$ and $d = 5$.
Substituting these values:
First term $(T_1)$ = $a = 8$
Second term $(T_2)$ = $a + d = 8 + 5 = 13$
Third term $(T_3)$ = $a + 2d = 8 + 2(5) = 8 + 10 = 18$
Fourth term $(T_4)$ = $a + 3d = 8 + 3(5) = 8 + 15 = 23$
Thus,the $A.P.$ is $8, 13, 18, 23, \ldots$
The general term $T_n$ is given by $T_n = a + (n-1)d = 8 + (n-1)5 = 8 + 5n - 5 = 5n + 3$.
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