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25 May, 16:39

a geometric series where the first term is - 12, the last term is - 972, and each term after the first is triple the previous term

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  1. 25 May, 17:04
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    the geometric series is a (n) = - 12 (3) ^ (n-1)

    Step-by-step explanation:

    "Triple" denotes multiplication by 3. Thus, the common factor here is 3.

    The general formula for a geometric series is a (n) = a (1) (r) ^ (n-1), where a (1) is the first term, r is the common ratio.

    Here, we have a (n) = (-12) (3) ^ (n-1) = - 972.

    We need to solve this for n, which represents the last term.

    The first step towards solving for n is to divide both sides by - 12:

    3^ (n-1) = 81

    To solve for n-1, rewrite 81 as 3^4. Then we have:

    3^ (n-1) = 3^4, implying that (n-1) = 4 and that n = 5.

    Then we know that it is the 5th term that equals - 972.

    In summary, the geometric series is a (n) = - 12 (3) ^ (n-1).
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