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 only 1 interaction.
If there are 3 children, there can be 5 interactions.
If there are 4 children, there can be 14 interactions.

Which recursive equation represents the pattern?

an = an – 1 + 2(n – 1)

an = an – 1 + (n – 1) 2

an = an – 1 + 2(n – 1)

an = an – 1 + (2n – 1)

Answer 1

\[an = an-1 + (n-1)^{2}\]

14 = 5 + (4-1)^2
5 = 1 + (3-1)^2