Question

If I have three consecutive integers and three consecutive even integers how would they be represented differently? Explain. ***Three consecutive integers can be represented as x, x+1, and x+2

Answer 1

9514 1404 393

Answer:

even integers differ by 2, consecutive integers differ by 1

Explanation:

Often problems involving consecutive integers use a variable (x) to represent the least of them. In that situation, ...

consecutive integers are x, x+1, x+2

consecutive even (or odd) integers are x, x+2, x+4.

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I often find it convenient to use the variable to represent the middle of the three integers. In that case, the representations are ...

consecutive integers: x-1, x, x+1

consecutive even (or odd) integers: x-2, x, x+2.

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In somewhat rare cases, you need to ensure that the integers are even, not odd, so the representation can be ...

consecutive even integers: 2n, 2n+2, 2n+4 . . . . where n is any integer