The sum S of the first n consecutive positive even integers is given by S=n(n+1)...

Question

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 ?

GMAT Panda · Accepted Answer

10 We translate the question’s phrase n(n+1) = 110 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 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

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

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