In each of the following,a and d for an A.P. | vedclass

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(A) The general form of an $A.P.$ is $a, a+d, a+2d, a+3d, \ldots$Given $a = \frac{15}{2}$ and $d = \frac{3}{2}$.First term $T_1 = a = \frac{15}{2} = 7

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$\frac{15}{2}, 9, \frac{21}{2}, 12, \ldots$

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(A) The general form of an $A.P.$ is $a, a+d, a+2d, a+3d, \ldots$Given $a = \frac{15}{2}$ and $d = \frac{3}{2}$.First term $T_1 = a = \frac{15}{2} = 7.5$.Second term $T_2 = a + d = \frac{15}{2} + \frac{3}{2} = \frac{18}{2} = 9$.Third term $T_3 = a + 2d = \frac{15}{2} + 2(\frac{3}{2}) = \frac{15}{2} + 3 = \frac{15+6}{2} = \frac{21}{2} = 10.5$.Fourth term $T_4 = a + 3d = \frac{15}{2} + 3(\frac{3}{2}) = \frac{15+9}{2} = \frac{24}{2} = 12$.Thus,the $A.P.$ is $\frac{15}{2}, 9, \frac{21}{2}, 12, \ldots$The general term is $T_n = a + (n-1)d = \frac{15}{2} + (n-1)\frac{3}{2} = \frac{15 + 3n - 3}{2} = \frac{3n + 12}{2}$.

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

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