Question

Achilles ordered a pizza with 16 slices. Every hour, he ate half of the remaining slices. Let f(n) be the number of slices Achilles ate in the hour since he got home.

Answer 1

Consider we need to find f(n).

Given:

Achilles ordered a pizza with 16 slices.

Every hour, he ate half of the remaining slices.

To find:

The function f(n) that is the number of slices Achilles ate in the hour since he got home.

Solution:

Initial number of slices = 16

Every hour, he ate half of the remaining slices. So, the number slices Achilles ate in the hour since he got home are:

8, 4, 2, 1, ...

It is a geometric sequence with first term 8 and common ratio
`(1)/(2)`.

The explicit formula for a geometric sequence is:

`f(n)=ar^(n-1)`

Where, a is the first term and r is the common ratio.

Substituting
`a=8,r=(1)/(2)`, we get

`f(n)=8\left((1)/(2)\right)^(n-1)`

Therefore, the function f(n) that is the number of slices Achilles ate in the hour since he got home is
`f(n)=8\left((1)/(2)\right)^(n-1)`.