Question

A school cafeteria sold 1,280 slices of pizza the first week, 640 the second week, and 320 the third week. If this pattern continues, in what week will the cafeteria sell 40 slices? Explain how you got your answer

Answer 1

In the sixth week the cafeteria sold 40 slices of pizza

Answer 2

the 6th week. The answer was computed using the geometric progression to establish the pattern of sales.

Explanation:

Given that the school cafeteria sold 1,280 slices of pizza the first week, 640 the second week, and 320 the third week. We may show this as a sequence

1280, 640, 320,......

From the pattern, we see that the next term is equivalent to the previous multiplied by 0.5. This is known as a geometric progression GP. The nth term of a GP is given as

Tn = ar^ (n-1)

where a is the first term. Tn is the nth term and r is the common ratio

40 = 1280 * 0.5^n -1

40/1280 = 0.5^n -1

(1/2)^5 = (1/2)^n -1

Comparing the powers,

5 = n - 1

n = 5 + 1

= 6

It means that the cafeteria sell 40 slices in the 6th week if the pattern continues