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    Word Problems: Consecutive Integer


    To solve word problems regarding consecutive integers, it is important to note:

    Consecutive Integers: n, n + 1, n + 2, ...

    Consecutive Even Integers: n, n + 2, n + 4, ... for even integer n

    Consecutive Odd Integers: n, n + 2, n + 4, ... for odd integer n
    Example #1:

    Find four consecutive even integers such that the sum of the second and fourth integers is one and a half times the sum of the first and third integers.

    Solution #1:

    Consecutive Even Integers: n, n + 2, n + 4, n + 6 for even integer n

    Sum of Second and Fourth Integers: (n + 2) + (n + 6) = 2n + 8

    Sum of First and Third Integers: n + (n + 4) = 2n + 4

    Since sum of the second and fourth integers is twice than the sum of the first and third integers, it follows that:

    2n + 8 = 1.5(2n + 4)

    2n + 8 = 3n + 6

    3n − 2n = 8 − 6

    n = 2

    ∴ Four consecutive even integers are 2, 4, 6, and 8
    Example #2:

    Find three consecutive odd integers such that the sum of the second and third integers is four times the first.

    Solution #2:

    Consecutive Even Integers: n, n + 2, n + 4 for odd integer n

    Sum of Second and Third Integers: (n + 2) + (n + 4) = 2n + 6

    Since sum of the second and third integers equals four times the first integer, it follows that:

    2n + 6 = 4n

    4n − 2n = 6

    2n = 6

    n = 3

    ∴ Three consecutive odd integers are 3, 5 and 7


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