Two students each write a function, S(n), that they think can be used to find the number of squares needed to make the nth figure in the pattern shown.

Use the drop-down menus to explain why each function does or does not represent the number of squares needed to make the nth figure in the pattern.

Answer choices:

Shara: S(1) = 2

S(n) = S(n − 1) ⋅ 2

This function _ be used to find the number of squares needed to make the nth figure in the pattern.

The number of squares needed to make each figure is_ the number of squares used in the previous figure.

Darren: S(n) = 2n

This function_ be used to find the number of squares needed to make the nth figure in the pattern.

The first figure has 2 squares, and you multiply by_ each time a figure is added. This repeated multiplication can be represented by an exponent.