Algebra question for growth and decay?

Question

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!

Answer 1

Best Answer - Chosen by Asker

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

Asker's Rating:

Asker's Comment:

Thank you!