Geometric Sequences and Series Practice & Key

Master geometric sequences and series with this Algebra 2 worksheet! Covers finding nth terms, common ratios, sigma notation, infinite series, applications, & key.

This comprehensive 4-page worksheet is designed to help Algebra 2 students master geometric sequences and series. It guides learners step-by-step from core definitions and sum formulas to evaluating finite sums, finding limits of infinite series, and solving real-world application problems.

What is Included:

Section A: Concept Check. Evaluates foundational understanding of constant ratios, explicit nth term formulas, finite series sum formulas, and the convergence conditions required for an infinite series to possess a finite sum.

Section B: Finding Terms. Focuses on identifying common ratios, calculating specific nth terms, writing explicit formulas, determining the term number (n) for a given value, and inserting missing geometric means.

Section C: Geometric Series. Covers calculating finite sums using sum formulas, evaluating sigma notation, solving for n given a total sum, finding the limits of infinite geometric series, and converting repeating decimals to fractions.

Section D: Applications. Challenges students to model real-world contextual scenarios using geometric sequences and series, featuring word problems on bouncing ball rebound distances, bacterial population growth, and exponential rumor spread.

Teacher Benefits:

Ready to Print & Go – Zero prep required. Excellent for structured lessons, homework, independent practice, or exam review.

Complete Solutions Included – Comes with a fully worked answer key detailing conceptual checks, explicit sequence formulas, expanded sigma calculations, infinite sum evaluations, and complete setups for all application word problems.