Question

Gary draws this sequence of patterns of white and grey squares. The sequence is continued. How many grey squares will there be with 16 white squares?

Answer 1

20 gray squares

Explanation:

Given

See attachment for squares

Required

Number of gray squares when white = 16

First, we calculate the equation that represents both squares.

The white squares

`a = 2` --- initial

`d = 4 - 2 = 6 - 4`

`d = 2` -- difference between successive gray squares

So, the nth term is:

`W_n = a + (n - 1)d`

`W_n = 2 + (n - 1)*2`

`W_n = 2 + 2n - 2`

`W_n = 2n`

The gray squares

`a = 6` --- initial

`d = 8-6=10-8`

`d = 2` -- difference between successive gray squares

So, the nth term is:

`G_n = a + (n - 1)d`

`G_n = 6 + (n - 1) *2`

`G_n = 6 + 2n - 2`

`G_n = 4 + 2n`

When the white squares is 16

`W_n = 16` --- Calculate n

`W_n = 2n`

`16 = 2n`

`8 = n`

`n = 8`

To get the number of gray squares;

Substitute
`n = 8` in
`G_n = 4 + 2n`

`G_n = 4 + 2 * 8`

`G_n = 20`