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Maths-

General

Easy

Question

The sum of the series $a minus open parentheses a plus d close parentheses plus open parentheses a plus 2 d close parentheses minus open parentheses a plus 3 d close parentheses plus horizontal ellipsis$ up to $left parenthesis 2 n plus 1 right parenthesis$ terms is

$- n d$
$a + 2 n d$
$a + n d$
$2 n d$

The correct answer is: $a plus n d$

$S equals open square brackets a minus open parentheses a plus d close parentheses close square brackets$ + $open square brackets open parentheses a plus 2 d close parentheses minus left parenthesis a plus 3 d right parenthesis close square brackets plus horizontal ellipsis plus open square brackets open parentheses a plus open parentheses 2 n minus 2 close parentheses d close parentheses close square brackets minus a plus left parenthesis 2 n minus 1 right parenthesis d right square bracket plus left parenthesis a plus 2 n d right parenthesis$
$equals open square brackets open parentheses negative d close parentheses plus open parentheses negative d close parentheses plus horizontal ellipsis plus n blank t i m e s close square brackets plus a plus 2 n d$
$equals negative n d plus a plus 2 n d$
$equals a plus n d$

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