Recursive Graphic Organizer

Identify whether a sequence is arithmetic (common difference) or geometric (common ratio) using the pattern row

Write the recursive and explicit formula for a given arithmetic or geometric sequence using the chart as a reference

Determine whether an infinite geometric series converges or diverges by comparing its ratio to 1

Distribute the chart at the start of a sequences-and-series unit as a standing reference rather than a worksheet, since all formulas are already filled in

Have students annotate their own worked examples next to each formula row to connect the abstract notation to practice problems

Pair the infinite-series convergence condition (r < 1 vs r ≥ 1) with a short set of practice items, since the chart states the rule but does not include practice problems

Sequence classification — students distinguish arithmetic from geometric sequences by their common difference or common ratio pattern.

Formula application — students use the recursive and explicit formulas provided to generate or extend sequence terms.

Series summation — students apply the finite-series sum formulas for both arithmetic and geometric series.

Convergence reasoning — students use the stated r < 1 / r ≥ 1 rule to determine whether an infinite geometric series converges.