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 \[n^\text{th}\] hour since he got it.
\[f\] is a sequence. What kind of sequence is it?
Choose 1 answer:
A
Arithmetic sequence
B
Geometric sequence
Write an explicit formula for the sequence.
\[f(n)=\]

Answer 1

B — Geometric sequence.

Each hour he eats half as much as the previous hour, so f(1)=8 and f(n+1)=½ f(n). Hence
f(n) = 8(1/2)^{\,n-1} (equivalently f(n)=16(1/2)^n).