Question

A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures 90 degrees: If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.)

What is the degree measure of the fifth slice Larry eats?


Can someone explain how they got the answer and what numbers to use?

Answer 1

9514 1404 393

Answer:

42°

Explanation:

The problem tells you the degree measures form an arithmetic progression. The sum of the 6 terms of the progression is 360, and the first term is 90.

The sum of n terms of an arithmetic progression is given by ...

Sn = (a1 +d/2(n -1))n

For Sn = 360, a1 = 90, n = 6, we have ...

360 = (90 +d/2(5))(6)

Dividing by 6 and subtracting 90 gives ...

-30 = 5/2d

Multiplying by 2/5, we find the number of degrees difference to be ...

d = -12

Then the 5th term of the sequence is ...

an = a1 +d(n -1)

a5 = 90 -12(5 -1) = 90 -48 = 42

The 5th slice Larry eats has a measure of 42 degrees.

_____

The slices measure 90, 78, 66, 54, 42, 30 degrees.