GMAT Number Properties Explained — Sum S of the first n consecutive positive even integers is given

The sum S of the first n consecutive positive even integers is given by S = n (n + 1) . For what value of n is this sum equal to 110 ?

consecutive integerssums of integersodds/evens

Explanation	Calculations	Help
$We translate the question’s phrase$	$n (n + 1) = 110$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We rewrite the expression in standard quadratic form by expanding and moving all terms to one side$	$n^{2} + n - 110 = 0$
$We factor the quadratic expression to find its roots$	$(n + 11) (n - 10) = 0$	Theory & Tactics Method Card EQUA2-B Click to view full details
$Since n represents a count of terms (and must be a positive integer), we discard the negative solution and take the positive one$	$n = 10$	Theory & Tactics Method Card TRANS4-B Click to view full details

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