Question

find the sum of all the terms of an AP 18, 15 1/2 , 13 ,....
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Answer 1

Step-by-step explanation:

$a \: = 18 \\ d = 15 \frac{1}{2} - 18 = - \frac {5}{2}$

$s(n) = \frac{n}{2} (2a + (n - 1)d) \\ \\ s(n) = \frac{n}{2} (2 \times 18 + (n - 1) \times ( - \frac{5}{2} )) \\ \\ s(n) = \frac{n}{2} (36 - \frac{5n}{2} + \frac{5}{2} ) \\ \\ s(n) = \frac{n}{2} ( \frac{72}{2} - \frac{5n}{2} + \frac{5}{2} ) \\ \\ s(n) = \frac{n}{2} ( \frac{72 + 5 - 5n}{2}) \\ \\ s(n) = \frac{n}{2} ( \frac{77 - 5n}{2} ) \\ \\s(n) = \frac{77n - 5n {}^{2} }{4}$

$put \: the \: number \: of \: terms \: in \: place \: of \: (n)$