Question

Suppose that $n, n+1, n+2, n+3, n+4$ are five consecutive integers. Determine a simplified expression for the sum of these five consecutive integers.

Answer 1

5n + 10

Explanation:

We need to add the five consecutive integers.

n + n + 1 + n + 2 + n + 3 + n + 4

Rearrange.

n + n + n + n + n + 1 + 2 + 3 + 4

Add.

5n + 10

Answer 2

5n + 10

Explanation:

We would like to find the sum of these 5 integers. Simply add them up:

n + (n + 1) + (n + 2) + (n + 3) + (n + 4) = 5n + (1 + 2 + 3 + 4) = 5n + 10

The answer is thus 5n + 10.

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