Question

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 1

The number of squares needed to make nth figure in the pattern is

S(n) = 2ⁿ.

According to the question,

S(1)=2; S(2) =4; S(3) = 8: S(4)=16 .........

S(1) = 2; S(2) = 2² = 4; S(3) = 2³ = 8; S(4) = 2⁴ = 16....... S(n) = 2ⁿ

In to find the number of squares needed to make the nth figure in the given pattern is S ( n ) = 2ⁿ.

Hence, the number of squares needed to make nth figure in the pattern is S(n) = 2ⁿ.