Students explore two fundamental number patterns — arithmetic sequences (adding a common difference) and geometric sequences (multiplying by a common ratio) — and learn to identify, extend, and describe each with a rule.
Students will be able to…
2, 4, 8, 16… or 2, 4, 6, 8… — both look like simple patterns, but they grow in completely different ways. How do you tell them apart and predict the next term?
Project this and sort each pattern or clue into arithmetic (add a difference) or geometric (multiply by a ratio).
Tap any phase to open the teacher moves and student actions.
2, 4, 6, 8 vs. 2, 4, 8, 16 — what’s the difference?
Teacher models.
Class uses Arithmetic or Geometric?
Students analyze sequences.
One sequence.
Aligned to the Common Core State Standards for Mathematics (High School: Algebra II).
Write arithmetic and geometric sequences recursively and explicitly.
Construct linear and exponential functions, including from sequences.
Recognize that sequences are functions defined on the integers.
Derive and use the formula for a geometric series.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students use formulas to find the sum of the first n terms of an arithmetic or geometric series. A printable sequences-and-series sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.