Sequences and Series Unit Plan | Arithmetic & Geometric Sequences

Overview: Equip your Algebra 2 or Precalculus students with a deep, visual understanding of sequences, series, and sigma notation with this comprehensive, ready-to-teach unit. This premium resource is designed to save you hours of planning while providing rigorous, step-by-step instruction that meets high school standards.

Every worked example includes full step-by-step algebraic working, and visual concepts such as bouncing ball heights, auditorium seating, and Pascal's Triangle feature clear, accurately labeled diagrams for maximum clarity.

### 📚 WHAT’S INCLUDED

**5 Topic Progressions of Visual Guided Notes:**

**Topic 1: Arithmetic Sequences** — Common difference, explicit/recursive formulas, term numbers, arithmetic means

**Topic 2: Arithmetic Series & Sigma Notation** — Partial sums, sigma introduction, evaluating/writing sigma, seating and salary applications

**Topic 3: Geometric Sequences** — Common ratio, explicit/recursive formulas, geometric means, exponential growth

**Topic 4: Geometric Series** — Partial sums, infinite series and convergence condition |r| < 1, sigma notation, bouncing ball and compound savings applications

**Topic 5: The Binomial Theorem** — Pascal's Triangle, Binomial Theorem formula, binomial coefficients, finding specific terms

**30-Problem Explicit & Recursive Formula Practice Set**

**20-Problem Arithmetic Series Drill**

**20-Problem Geometric Series Drill**

**25-Problem Sigma Notation Translation & Evaluation Set**

**Infinite Geometric Series Convergence Guided Activity** — Explores why |r| < 1 is required and derives the infinite sum formula

**15-Problem Binomial Theorem Expansion Set**

**20 Real-World Application Problems** — Includes full worked solutions and labeled diagrams

**Cumulative Unit Review**

**Comprehensive Unit Test** — Multiple choice, short answer, and free response

**Complete Answer Key with All Working** — Step-by-step logic for every calculation, sum, and convergence determination

### 🎯 SKILLS COVERED

Identifying common differences and common ratios Writing and evaluating explicit formulas: \(a_n = a_1 + (n-1)d\) and \(a_n = a_1r^{\,n-1}\) Writing and evaluating recursive formulas Finding specific terms and term numbers Calculating arithmetic and geometric means Calculating partial sums for arithmetic and finite geometric series Determining convergence and evaluating infinite geometric series Translating between expanded series and sigma notation Evaluating expressions written in sigma notation Expanding binomials using Pascal's Triangle and the Binomial Theorem formula Finding specific terms in binomial expansions Applying sequences and series to real-world contexts such as compound interest, depreciation, physics/bouncing, and seating

### 💡 HOW TO USE

Use the **Visual Guided Notes** for direct instruction to introduce each of the 5 topics.

Assign the **Practice Sets and Drills** for targeted homework or in-class practice.

Implement the **Convergence Guided Activity** as a collaborative discovery lesson.

Use the **Real-World Application Problems** as extension activities, group work, or formative assessments.

Assign the **Cumulative Review** prior to the Unit Test.

### 🎓 GRADE SUITABILITY

Grades **10–12**, specifically aligned to Algebra 2 and Precalculus curricula.

### 📐 TPT CATEGORY & DETAILS

**Category:** Math **Sub-category:** Algebra 2 / PreCalculus **Resource Type:** Unit Plans, Worksheets, Activities, Assessment **Grade Levels:** 10th, 11th, 12th

### 📏 STANDARDS ALIGNMENT

**CCSS.HSF.BF.A.2:** Write arithmetic and geometric sequences both recursively and with an explicit formula.

**CCSS.HSF.LE.A.2:** Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

**CCSS.HSA.SSE.B.4:** Derive the formula for the sum of a finite geometric series and use the formula to solve problems.

**CCSS.HSA.APR.C.5:** (+) Apply the Binomial Theorem for the expansion of \((x + y)^n\).