Find the sum of $25 t h$ of an $A P$ which nth term is given by $t_{n} = (7 - 3 n)$

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Solution

The $n^{t h}$ term is given as $t_{n} = 7 - 3 n$

$t_{1} = 7 - 3 (1) = 4$

$t_{2} = 7 - 3 (2) = 1$

$t_{3} = 7 - 3 (3) = - 2$

This shows that the first term is 4 and the common difference is $- 3$ .

The sum of the 25 terms of an A.P. is,

$S_{25} = \frac{25}{2} [2 (4) + (25 - 1) (- 3)]$

$= \frac{25}{2} (- 64)$

$= - 800$

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