Geometric Sequences
I can find the common ratio of a geometric sequence and write a rule for any term.
What students learn
Students learn to divide to find the common ratio r, test a second pair, and use aₙ = a₁ · rⁿ⁻¹ to find any term.
See inside
The key rule
Find r by dividing a term by the one before, not by subtracting, and check a second pair.
aₙ = a₁ · rⁿ⁻¹
A difference that changes from pair to pair is not an arithmetic rule.
Watch out
For 2, 10, 50, 250, ... a student subtracts to find the rule.
The mistake: 10 − 2 = 8, so add 850 − 10 = 40, not 8: the gap changes.
The fix: 10 ÷ 2 = 5 and 50 ÷ 10 = 5, so r = 5Dividing gives 5 on both pairs.
The mistakes it targets
- Subtracts instead of dividing to find the common ratio
- Uses n factors of r instead of n − 1
- Stops at r³ instead of taking the cube root
- Loses the sign of a negative common ratio
- Makes an even power of a negative ratio negative
The interactive Teacher Deck (33 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (five steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, five common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.