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28 August, 06:57

Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. - 2, 6, - 18, 54, ...

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  1. 28 August, 08:19
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    Step-by-step explanation:

    In a geometric sequence, the consecutive terms differ by a common ratio, r. Considering the given sequence,

    r = 6 / - 2 = - 18/6 = - 3

    Therefore, the sequence is geometric.

    The formula for determining the nth term of a geometric progression is expressed as

    Tn = ar^ (n - 1)

    Where

    a represents the first term of the sequence.

    r represents the common ratio.

    n represents the number of terms.

    From the information given,

    a = - 2

    r = - 3

    The explicit formula is

    Tn = - 2 * ( - 3) ^ (n - 1)

    To find the 8th term, T8,

    T8 = - 2 * ( - 3) ^ (8 - 1)

    T8 = - 2 * ( - 3) ^7

    T8 = - 2 * - 2187

    T8 = 4374
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