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?

an = an - 1 + 3 (n - 1)

an = an - 1 + 3 (n - 1)

an = an - 1 + (3n - 1)

an = an - 1 + (n - 1) 3

Question

Isaias Watkins

Mathematics

24 October, 23:55

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?

an = an - 1 + 3 (n - 1)

an = an - 1 + 3 (n - 1)

an = an - 1 + (3n - 1)

an = an - 1 + (n - 1) 3

+2

Answers (1)

Know the Answer?

Leonardo Tran · Answer 1

From your situations given:

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.

The equation would be an = an - 1 + 3 (n - 1)