Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Model a geometric situation with explicit and recursive rules
Problem
A population starts at \(80\) and doubles each period. Write both the explicit and recursive geometric-sequence rules.
Big Picture
What this problem is really about
The context describes a geometric sequence when each period scales the entire previous population by the same factor. We’ll define the indexed population, identify its starting value and common ratio, and encode that structure once by counting all factor applications and once by updating from the preceding period. Agreement at the next period verifies both forms.
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