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13 October, 05:02

A sequence is defined recursively by f (1) = 6 and f (n) = f (n-1) + 2n. Find f (4)

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  1. 13 October, 06:17
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    Since we have given the value of f (1) = 6 at n = 1, we proceed n = 2, 3 and 4 to reach f (4).

    At n = 2,

    f (2) = f (2 - 1) + 2 (2)

    f (2) = f (1) + 4

    f (2) = 6 + 4

    f (2) = 10

    At n = 3,

    f (3) = f (3 - 1) + 2 (3)

    f (3) = f (2) + 6

    f (3) = 10 + 6

    f (3) = 16

    Notice that it follows the sequence: 6, 10, 16 by just adding 6. Thus,

    f (4) = 16 + 6

    f (4) = 22
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