Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
F 301. Extend a given pattern by a few terms for patterns that have a constant factor between terms
F 703. Exhibit knowledge of geometric sequences
F 502. Find the next term in a sequence described recursively
F 603. Find a recursive expression for the general term in a sequence described recursively
F 702. Build functions for relations that are exponential
A 512. Work problems involving positive integer exponents
AF 601. Solve word problems containing several rates, proportions, or percentages
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F 301. Extend a given pattern by a few terms for patterns that have a constant factor between terms
F 703. Exhibit knowledge of geometric sequences
F 502. Find the next term in a sequence described recursively
F 603. Find a recursive expression for the general term in a sequence described recursively
F 702. Build functions for relations that are exponential
A 512. Work problems involving positive integer exponents
AF 601. Solve word problems containing several rates, proportions, or percentages
What you'll learn
- Write the explicit rule `aₙ = a₁·r^(n−1)` for a geometric sequence and use it to find any term, and use `Sₙ = a₁(1 − rⁿ)/(1 − r)` to find the sum of the first `n` terms
- Test whether a sequence is geometric by computing all consecutive ratios, state the common ratio including when it is negative or fractional, and distinguish a geometric sequence (exponential in its index) from an arithmetic one (linear)
- Write the recursive rule `aₙ = r·aₙ₋₁` (with `a₁` stated) and distinguish it from the explicit rule
- Find `r`, `a₁`, or a missing term from two given terms, recognizing when an even gap count admits two possible ratios
- Determine whether an infinite geometric series converges by testing `|r| < 1`, and compute `S∞ = a₁/(1 − r)` when it does
- Translate a percentage growth or decay rate into a common ratio and solve ACT-style compound-interest, half-life, and depreciation problems
Slides
Step through the lesson, or watch it as a narrated video
Slides
In development
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