Find the sum of the first 25 terms of an A.P. whose nth term is given by $a_{n} = 2 - 3 n$ .

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Solution

Given that, $a_{n} = 2 - 3 n$

Putting the value of $n = 1$ ,then
$a_{1} = 2 - (3 \times 1)$
$= 2 - 3 = - 1$

Putting the value of $n = 2$ ,then
$a_{2}$ $= 2 - (3 \times 2)$
$= 2 - 6$
$= - 4$

Therefore, $a = - 1$ and $d = - 4 - (- 1) = - 4 + 1 = - 3$

$S_{n} = \frac{n}{2} (2 a + (n - 1) d)$

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

= $\frac{25}{2} [- 2 - 72]$

= $\frac{25}{2} \times (- 74)$

= $25 \times (- 37)$

= $- 925$

Therefore, sum of first $25$ term is $- 925$

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