Advanced Algebra

A playground is being designed where children can interact with their friends in certain combinations.
If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 1 interactions.
If there are 3 children, there can be 4 interactions.
If there are 4 children, there can be 9 interactions.
Which recursive equation represents the pattern?

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  2. 👎 0
  3. 👁 1,713
  1. a(1) = 0
    a(n+1) = a(n)+(2n-1)

    or,

    a(n) = (n-1)^2

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  2. Thank you

    Could it be written as a(n)=a(n-1)+2^n-3

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  3. Did you even check out your idea?

    a(1) = 0
    a(2) = a(1) + 2^2-3 = 0+1 = 1
    a(3) = a(2) + 2^3-3 = 1+5 = 6
    a(4) = a(3) + 2^4-3 = 6+13 = 19

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