RECURSIVE RULE! for the sequence 2, 4, 12, 48, 240?

recursive rule for the following sequence…

it goes up by: 2×2=4, 4×3=12, 12×4=48, 48×5=240 etc.

2,4,12,48,240

4 Answers

  • Recursive formula:

    a(n) = n * a(n-1)

    a(1) = 1 * 2

    a(2) = 2 * a(1)

    a(3) = 3 * a(2)

    a(4) = 4 * a(3)

    a(5) = 5 * a(4)

    etc.

    Closed formula:

    a(n) = 2*(n!)

    a(1) = 2 * (1) = 2

    a(2) = 2 * (2 * 1) = 4

    a(3) = 2 * (3 * 2 * 1) = 12

    a(4) = 2 * (4 * 3 * 2 * 1) = 48

    a(5) = 2 * (5 * 4 * 3 * 2 * 1) = 240

    etc.

  • Each one is climbing up the numerical sequence.

  • a(1) = 2

    a(n) = n * a(n-1)

    In other words, the closed formula is

    a(n) = 2 * n!

  • no you double the # everytime!

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