Unit 09 · 3 Weeks · 7 Lessons
Sequences, Series & the Binomial Theorem
How do recursive and explicit rules describe patterns, accumulated change, and finite or infinite sums?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Arithmetic Sequences: Explicit & Recursive Forms
Arithmetic sequences have constant first differences. Explicit form gives direct access; recursive form emphasizes step-by-step generation.
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Lesson 02Geometric Sequences: Growth, Decay & Recursion
Geometric sequences have a constant ratio. The sign and magnitude of r determine growth, decay, and alternation.
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Lesson 03General Sequences, Patterns & Difference Tables
Sequence rules may be explicit, recursive, piecewise, or generated by patterns. Constant kth differences suggest a degree-k polynomial model.
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Lesson 04Finite Arithmetic & Geometric Series
A series is a sum of sequence terms. Formula choice depends on additive or multiplicative structure.
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Lesson 05Infinite Geometric Series & Convergence
An infinite geometric series converges only when repeated terms shrink toward zero. Otherwise partial sums do not approach a finite limit.
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Lesson 06Sigma Notation & Summation Properties
Sigma notation compresses sums. Properties allow constants to factor out and sums to split, but bounds and index meaning must remain clear.
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Lesson 07Pascal’s Triangle & the Binomial Theorem
Pascal’s Triangle and combinations provide coefficients for binomial expansion. Term structure can be predicted without expanding every term.
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Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Sequence, Series & Repeated-Change Analysis
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.