Question

The sum of the first n consecutive even numbers can be found using S = n2 + n, where n > 2. What is the value of n when the sum is 30?

Answer 1

The value of n when the sum is 30 is equal to 5.

Given the following data:

• Sum, S = 30

To determine the value of n when the sum is 30:

How to calculate the sequence of numbers.

Mathematically, the sum of the first n consecutive even numbers is given by this formula:

$S=n^2+n$

Where:

• S is the sum.

• n is the consecutive even numbers.

Substituting the given parameters into the formula, we have;

$30=n^2+n\\\\n^2+n-30=0\\\\n^2 +6n-5n-30=0\\\\n(n+6)-5(n+6)=0\\\\(n+6)(n-5)=0$

n = -6 or 5.

Since, n > 2;

n = 5.

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