Geometric Sequences & Series Worksheet | Formulas, Sums & Applications

This in-depth Algebra 2 Worksheet on Geometric Sequences and Series provides students with rigorous, well-structured practice aligned to Common Core Standard HSF.BF.A.2. It covers everything from writing recursive and explicit formulas to calculating finite and infinite geometric series, with a strong focus on application and real-world problem solving.

The worksheet is ideal for classroom instruction, independent practice, homework, test prep, or substitute plans. It includes 10 problems per section across six distinct parts, ensuring students build both skill fluency and conceptual understanding.

All content is 100% editable, making it easy to tailor to your students' needs or pacing, and an answer key is included for efficient grading or self-checking.

What's Included:

• Full-length worksheet (60 problems total, approximately 90–120 minutes of work)
• Editable format for customization
• Complete answer key
• Clear section titles and problem variety
• Mix of numerical, algebraic, and application-based problems
• Print-friendly layout

Worksheet Structure:

Part A: Warm-Up & Review (10 Questions)
Covers foundational skills such as exponents, square roots, and basic sequence identification.

Part B: Identifying Terms in Geometric Sequences (10 Questions)
Practice calculating specific terms given a_1 and r using the geometric formula.

Part C: Writing Formulas (10 Questions)
Develop both recursive and explicit formulas for a variety of sequences.

Part D: Application & Modeling (10 Questions)
Solve real-world problems involving geometric growth and decay, including population and financial contexts.

Part E: Finite Geometric Series (10 Questions)
Use the formula S_n = a_1*(1 - r^n)/(1 - r) to calculate sums of geometric series.

Part F: Infinite Geometric Series (10 Questions)
Determine convergence and calculate sums using S = a_1 / (1 - r).

Standards Alignment:

• Common Core: HSF.BF.A.2 – Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
• Also supports TEKS and VA SOL objectives related to sequences and series.

Ideal For:

• Algebra 2 teachers and intervention specialists
• Review before assessments or standardized tests
• Homework packets or flipped classroom activities
• Sub plans or emergency lesson prep
• Homeschool instruction or tutoring programs

What Teachers Are Looking For:
geometric sequences, geometric series, explicit formula, recursive formula, finite and infinite series, HSF.BF.A.2, Algebra 2 sequences, math worksheet editable, common core aligned algebra

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