Scott’s Workout

Learning Focus

Model a sequence with a table, graph, and explicit/recursive equations. Decide if it is arithmetic, geometric, or neither.

Big idea

If Scott’s daily push-ups increase by the same amount each day, the model is arithmetic.

Worked example

Day 1: 3 push-ups, and he adds 2 each day.

• Recursive: $f(n)=f(n-1)+2$, $f(1)=3$
• Explicit (with day $n$): $f(n)=3+2(n-1)=2n+1$
• Day 10: $2(10)+1=21$

Takeaways

• Spot the common difference in tables and graphs (constant slope).
• Explicit forms answer “any day” questions quickly.