Question

A patteren is shown below what is the patteren rule? How many cubes are in the tenth image if the patteren contiues ? How about the 100th image show your thinking below

Answer 1

a) Pattern rule = 2n - 1

b) Tenth image = 19 cubes

c) 100th image = 199 cubes

Step-by-step explanation

We need to first see that the number of cubes increase in a steady pattern

1 cube

3 cubes

5 cubes

7 cubes

We can see that the number of cubes increases like an arithmetic progression with

First term = a = 1

Common difference = d = 2

The nth term of an arithmetic progression is given as

nth term = a + (n - 1)d

a = first term = 1

d =common difference = 2

n = number of terms

nth term = 1 + (n - 1)2

nth term = 1 + 2n - 2

nth term = -1 + 2n = 2n - 1

b) The 10th term

n = 10

10th term = 2n - 1 = 2(10) - 1 = 20 - 1 = 19 cubes

c) 100th image

n = 100

100th image = 2n - 1 = 2(100) - 1 = 200 - 1 = 199 cubes

Hope this Helps!!!