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Algebra question for growth and decay?

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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, ...show more
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an = an – 1 + 3(n – 1)
--------------------------------
verify:
a3=9
a4 = a3+3(4-1)
a4 = 9 +3(3) = 18

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Algebra question for growth and decay?
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 3 interactions.
If there are 3 children, there can be 9 interactions.
If there are 4 children, there can be 18 interactions.

Which recursive equation represents the pattern?

A. an = an – 1 + (n – 1)^3
B. an = an – 1 + 3^(n – 1)
C. an = an – 1 + 3(n – 1)
D. an= an – 1 + (3n – 1)


i know that if their are 9 children their would be 108 interactions. But I have no idea about this formula. Please help!
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