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12 August, 12:12

81, 27, 9, 3, ... Find the common ratio of the given sequence, and write an exponential function which represents the sequence. Use n = 1, 2, 3, ...

A) 3; f (n) = 81^n-1

B) 3; f (n) = 81 (3) ^n-1

C) 1 / 3; f (n) = 81 (3) ^n-1

D) 1 / 3; f (n) = 81 (1 / 3) ^n-1

Answer -

Since each term is multiplied by 1/3to get to the next term, the common ratio is 1/3. The common ratio is also the base of anexponential function. The correct answer is1/3; f (n) = 81 (1/3) ^n-1

so D.

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Answers (1)
  1. 12 August, 12:22
    0
    Given Sequence:

    81, 27, 9, 3, ...

    To find the common ratio:

    Common ratio, r = a2/a1

    r = 27/81

    r=1/3

    r = a3/a2 = 9/27 = 1/3

    r = a4/a3 = 3/9 = 1/3

    So common ratio is 1/3.

    Now exponential function is:

    f (n) = 81 (1/3) ^ (n-1)

    When n=1

    f (1) = 81 (1/3) ^ (1-1)

    f (1) = 81 (1/3) ^0

    f (1) = 81 (1) = 81

    When n=2

    f (2) = 81 (1/3) ^ (2-1)

    f (2) = 81 (1/3) ^1

    f (2) = 27

    And so on.

    Answer: Option D. r = 1/3, f (n) = 81 (1/3) ^n-1
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