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 4 interactions.
If there are 4 children, there can be 9 interactions.

Which recursive equation represents the pattern?

an = an – 1 + 3n – 2

an = an – 1 + 2n – 3

an = an – 1 + (3n – 2)

an = an – 1 + (2n – 3)

Answer 1

a_n = a_n – 1 + 3^n – 2

a_n = a_n – 1 + 2^n – 3

a_n = a_n – 1 + (3n – 2)

a_n = a_n – 1 + (2n – 3)

Answer 2

Nvm I found it, it was D

Answer 3

Yep!

Answer 4

\(\large a_{n-1} = (n-2)^2\)

\(\large \implies a_{n} = (n-1)^2 = a_{n-1}-(-2n+3)\)