# 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...
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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, 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!

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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