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24 August, 00:23

The 3rd term of an arithmetic sequence is - 1 and the 7th term is - 13. Find the explicit formula for this sequence. What is a22?

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  1. 24 August, 02:45
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    Hopefully the math terms won't confuse anyone.

    So in the series, a_3 = - 1 and a_7 = - 13. Since it's an arithmetic sequence, all the terms in the series can be represented as:

    a_n = a_0 + n * k

    where n is the nth number. K is a constant you add to reach the next term, and a_0 is the starting constant.

    a_7 = a_0 + 7 * k

    a_3 = a_0 + 3 * k

    solving this system gives you that

    k = - 3 and a_0 = 8

    Hence:

    a_22 = 8 + 22 * - 3 = - 58
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