Final answer:
The second smallest slice has a volume of 1/3. The fifth smallest slice also has a volume of 1/3.
(a) The common ratio of the sequence is 1.
Step-by-step explanation:
To find the second smallest slice of the pie, we need to determine the common ratio of the geometric sequence. Since the smallest slice has a volume of 1/3 of the whole pie, we can express it as 1/3.
The second smallest slice is obtained by multiplying the first slice by the common ratio. Let's call the common ratio 'r'. Therefore, the volume of the second smallest slice is (1/3) x r.
Similarly, the volume of the fifth smallest slice can be expressed as (1/3) x r^4, since we're multiplying the first slice by the common ratio four times.
(a)To find the common ratio, we can set up an equation using the information given. Since the volume of each slice forms a geometric sequence, we can write:
(1/3) x r = (1/3) x r^4
Dividing both sides of the equation by (1/3), we get:
r = r^4
Dividing both sides by r^4, we get:
1 = r^3
Taking the cube root of both sides:
r = 1
Therefore, the common ratio of the sequence is 1. Using this information, we can find the volume of the second smallest slice and the fifth smallest slice:
The volume of the second smallest slice is (1/3) x r = (1/3) x 1 = 1/3.
The volume of the fifth smallest slice is (1/3) x r^4 = (1/3) x 1^4 = 1/3.