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18 September, 05:22

Write a formula for the general term (the nth term) of the arithmetic sequence shown below. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.

a1 = - 13, d = - 5

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  1. 18 September, 05:25
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    an = a1 + (n-1) * d

    a20 = - 108

    Step-by-step explanation:

    For the arithmetic sequence

    a1 = - 13, d = - 5

    a2 = a1 + d (where d is the ratio of the sequence)

    a2 = - 13 - 5

    a2 = - 18

    a3 = a2 + d

    But a2 = a1 + r

    a3 = a1 + 2r = - 13 + 2 (-5) = - 23

    So: an = a1 + (n-1) * d

    a20 = - 13 + 19 * (-5)

    a20 = - 108
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