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 $\dfrac{1}{2}$.

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 $a=8,r=\dfrac{1}{2}$, we get

$f(n)=8\left(\dfrac{1}{2}\right)^{n-1}$

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