Calculate the sum of the series $14 + 11 + 8 + 5 + . . . + - 82$ .

1122

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1022

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- 1022

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- 1122

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Solution

The correct option is B $- 1122$
First term = $a = 14$
last term, $l = - 82$
$a_{n} = - 82$
Common difference = -3
$a_{n} = a + (n - 1) d$
$- 82 = 14 + (n - 1) (- 3)$
$- 82 - 14 - 3 = - 3 n$
$- 99 = - 3 n$
$n = 33$
$S_{n} = \frac{n}{2} [a + l]$
$S_{33} = \frac{33}{2} [14 + (- 82)]$
$S_{33} = 16.5 [- 68]$
$S_{33} = - 1122$

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