Let n be the middle number of three consecutive integers

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Let n be the middle number of three consecutive integers

This means:

• n is the second of three consecutive integers
• The first consecutive integer is n - 1
• The third consecutive integer is n + 1

The sum is found by:
n - 1 + n + n + 1

Simplifying, we get:
(n + n + n) + 1 - 1
3n