Learning Goal
Arithmetic sequences and series
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 201. Extend a given pattern by a few terms for patterns that have a constant increase or decrease between terms
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
A 406. Exhibit knowledge of slope
A 514. Determine the slope of a line from an equation
F 503. Build functions and use quantitative information to identify graphs for relations that are proportional or linear
AF 503. Match linear equations with their graphs in the coordinate plane
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F 201. Extend a given pattern by a few terms for patterns that have a constant increase or decrease between terms
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
A 406. Exhibit knowledge of slope
A 514. Determine the slope of a line from an equation
F 503. Build functions and use quantitative information to identify graphs for relations that are proportional or linear
AF 503. Match linear equations with their graphs in the coordinate plane
What you'll learn
- Write the explicit rule `aₙ = a₁ + (n − 1)d` for an arithmetic sequence and use it to find any term, and use `Sₙ = (n/2)(a₁ + aₙ)` to find the sum of the first `n` terms
- Test whether a sequence is arithmetic by computing all consecutive differences, and state the common difference, including when it is negative
- Write the recursive rule `aₙ = aₙ₋₁ + d` (with `a₁` stated) and distinguish it from the explicit rule
- Find `d`, `a₁`, or a missing term given any two terms, by counting the gaps between their positions
- Identify an arithmetic sequence as a linear function of its index, with `d` as the slope
- Solve ACT-style word problems that model a repeating fixed increase, distinguishing requests for a term from requests for a sum
Slides
Step through the lesson, or watch it as a narrated video
Slides
In development
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