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18 April, 07:48

How menu terms are in the arithmetic sequence 7,0,-7, ...,-175?

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  1. 18 April, 08:26
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    27 terms

    Step-by-step explanation:

    Here the first term is 7 and the common difference is - 7. Each new term is equal to the previous term, less 7.

    The general formula that involves first and last terms, common difference and number of terms is last = first + (n - 1) (common difference)

    We substitute the knowns, as follows:

    -175 = 7 + (n-1) (-7)

    Solve this first for n-1, and then for n:

    Subtract 7 from both sides: - 182 = - 7 (n-1)

    Dividing both sides by - 7 yields 26 = n - 1

    Then n = 27.

    There are 27 terms in this arith. sequence.
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