Ask Question
20 April, 17:02

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

+4
Answers (1)
  1. 20 April, 17:15
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. - 2, 6, - 18, 54, ... ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers