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15 October, 06:35

How do you find the nth to the quadratic sequence of 3,8,15,24,35

Answers (1)
  1. M
    15 October, 07:11
    0
    Having the first term of the sequence

    a (0) = 3

    a (1) = 3+5=8

    We realized that

    a (1) = a (0) + 2⋅2+1

    We also have:

    a (2) = a (1) + 2⋅3+1=8+7=15

    a (3) = a (2) + 2⋅4+1=15+9=24

    From above we can realize that each term is the sum of the previous

    term and 2 * (sequence coefficient added to 1) and 1

    So the nth term will be:

    a (n) = a (n-1) + 2⋅ (n+1) + 1
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