Question

Stella is using grid paper to make shapes. Her first shape has an area of 14 square units. Her second shape has an area of 28 square units. Her third shape has an area of 42 square units. If this pattern continues what will be the area of her fourth shape

Answer 1

28÷14=42-28=14+42=56

Answer 2

56

Explanation:

The pattern is an arithmetic sequence:

by the first three terms, the common difference is:

28-14=42-28=14

So the next pattern would be:

14+42=56

By the equation x = a + d ( n - 1 )

Substituting when n=1, x=14 and when n=2 x=28

a = 14 and d = 14

x = 14 + 14 ( n - 1 )

substituting n = 4

x = 14 + 14 ( 4 - 1 )

x = 56