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5 November, 13:32

What is a40 for the arithmetic sequence presented in the table below?

n 8 12

an 60 48

Hint: an = a1 + d (n - 1), where a1 is the first term and d is the common difference

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  1. 5 November, 13:50
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    Lets first get the common difference = d.

    Using,

    an = a1 + d (n-1)

    a8 = a1 + d (8-1)

    60 = a1+7d

    a12 = a1 + d (12-1)

    48 = a1 + 11d

    from these 2 equations we will get a1, d

    subtracting them, we get

    60-48 = 7d-11d = - 4d

    12 = - 4d

    d = - 3.

    and

    60 = a1 + 7d = a1 + 7 (-3) = a1 - 21

    a1 = 60+21 = 81.

    now a40 = a1 + d (40-1) = 81 + (-3) 39

    a40 = - 36.
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