What is the sum of the geometric sequence 2, 8, 32, … if there are 8 terms? 21,845 43,690 65,535 87,380

Question

What is the sum of the geometric sequence 2, 8, 32, … if there are 8 terms? 21,845
43,690
65,535
87,380

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2022-04-28T23:10:34+00:00 1 Answer 0

Answers ( 1 )

  1. Faith
    0
    2022-04-28T23:12:07+00:00

    Answer:

    The answer is B. 43,690

    Step-by-step explanation:

    S = 2 * 4^0 + 2 * 4^1 + 2 * 4^2 + … + 2 * 4^7

    S * 4 = 2 * 4^1 + 2 * 4^2 + … + 2 * 4^7 + 2 * 4^8

    4S – S = 2 * 4^8 – 2 * 4^0

    3S = 2 * (4^8 – 1)

    S = (2/3) * (4^8 – 1)

    S = (2/3) * (2^16 – 1)

    S = (2/3) * (65535)

    S = 43690

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