Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Construct a recursive arithmetic sequence rule
Problem
Construct the recursive arithmetic-sequence rule when the first week has \(20~\text{pushups}\) and each week adds \(5~\text{pushups}\).
Big Picture
What this problem is really about
A recursive sequence rule needs both an anchor and an update; either part alone leaves the sequence incomplete. We’ll translate the first week into the initial condition and the fixed weekly increase into an operation on the previous term. Generating several early terms will verify the direction and size of the repeated change.
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