Question

Kaya claims that 8n is the number of dots in figure n. Kiana claims that the number of dots in figure n is given by 2(n+1)
`^(2)^-2(n--1)^(2)`

Consider the square arrangements below in relation to the girls' expressions, where n represents the figure number. Determine whether Kaya, Kiana or both girls are correct in their given expressions. Justify your response.


The evaluation of your response will be based on the following criteria.

Correctly identifying which girl is correct in their given expressions while showing your work.
Explaining your reasoning.
Answer the question in two to three sentences.

HINT: Plug in each figure number for n in both girl's expressions

Answer 1

Kaya's answer is correct.

Explanation:

The number of dots in successive figures are

8, 16, 24.

So Kaya's solution 8n is correct.

When n = 1, first square = 8*1 = 8 dots

n = 2: second square = 8*2 = 16

n = 3, 3rd square = 8*3 = 24.

If I have interpreted Kianna's formula correctly

for n = 1, then the number of dots = 2(1+ 1)^2 - 2(1 - - 1)^2

= 0.