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19 August, 12:24

Write a recursive and an explicit formula to represent the following sequence 52, 40, 28, 16, ...

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  1. 19 August, 12:48
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    Explicit tn = 52 + (n - 1) * (-12)

    Recursive = tn = t (n - 1) - 12

    Step-by-step explanation:

    The difference between term n and term n - 1 is can be found by taking the difference between and 2 consecutive terms.

    t3 = 28

    t2 = 40

    d = t3 - t2

    d = 28 - 40

    d = - 12

    Explicit

    tn = a1 + (n - 1) * d

    a1 = 52

    d = - 12

    tn = 52 + (n - 1) * (-12)

    Example

    Find t5

    t5 = 52 + (5 - 1) * (-12)

    t5 = 52 + 4 * - 12

    t5 = 52 - 48

    t5 = 4

    Recursive

    tn = t (n - 1) - 12

    Example

    t5 = t4 - 12

    t5 = 16 - 12

    t5 = 4 just as it did before.
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