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13 February, 01:27

The recursive function for a sequence is given below.

f (1) = 200

f (n) = 2 · f (n - 1), for n = 2, 3, 4, ...

What is the 5th term of this sequence?

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Answers (2)
  1. 13 February, 01:42
    0
    Answer: 6400

    Step-by-step explanation:

    Given:

    f (1) = 200

    f (n) = 2. f (n-1), for n = 2,3, 4, ...

    To find the 5th term

    when n = 2, the sequence becomes

    f (2) = 2. f (2-1)

    f (2) = 2 f (1)

    since f (1) = 200

    therefore:

    f (2) = 2 x 200

    f (2) = 400

    When n = 3

    f (3) = 2f (2)

    f (3) = 2 x 400

    f (3) = 800

    When n = 4

    f (4) = 2 f (3)

    f (4) = 1600

    When n = 5

    f (5) = 2f (4)

    f (5) = 3200

    When n = 6

    f (6) = 2f (5)

    f (6) = 6400

    Since n = 2, 3, 4 ... this means that the 5th term if f (6), therefore, the 5th term is 6400
  2. 13 February, 01:45
    0
    f (5) = 3200

    Step-by-step explanation:

    Using the recursive formula to generate the terms, that is

    f (2) = 2 * f (1) = 2 * 200 = 400

    f (3) = 2 * f (2) = 2 * 400 = 800

    f (4) = 2 * f (3) = 2 * 800 = 1600

    f (5) = 2 * f (4) = 2 * 1600 = 3200
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