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jarptica [38.1K]
3 years ago
10

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

ith 16 white squares?
Mathematics
1 answer:
zzz [600]3 years ago
4 0

Answer:

20 gray squares

Step-by-step explanation:

Given

See attachment for squares

Required

Number of gray squares when white = 16

First, we calculate the equation that represents both squares.

<u>The white squares</u>

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

<u>The gray squares</u>

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

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