Growing Dots

Learning Focus

Describe a growing pattern with tables, graphs, and equations.

Big idea

An arithmetic sequence changes by a constant difference $d$ each step.

• Recursive: $f(n)=f(n-1)+d$ with a start value
• Explicit: $f(n)=f(0)+dn$ (or an equivalent form with your indexing)

Worked example

If a pattern has $4$ dots at minute $0$ and adds $3$ dots each minute:

• Recursive: $f(t)=f(t-1)+3$, $f(0)=4$
• Explicit: $f(t)=4+3t$
• At $t=100$: $f(100)=304$

Takeaways

• Tables, graphs, and equations should tell the same story.
• Constant difference $\Rightarrow$ arithmetic sequence / linear family.