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 12 interactions.
If there are 4 children, there can be 39 interactions.

Which recursive equation represents the pattern?

Answer 1

an = an – 1 + 3(n – 1)

an = an – 1 + 3(n – 1)

an = an – 1 + (3n – 1)

an = an – 1 + (n – 1)3