Sequences, Series & Probability
Explore arithmetic and geometric sequences, sigma notation, the Binomial Theorem, counting principles, and probability — the mathematics of patterns, sums, and chance.
Estimated Time
4–5 weeks
Difficulty
Intermediate
Overview
Unit description, learning objectives, and skills.
Unit 11 — Sequences, Series & Probability is the mathematics of patterns and chance. You will write arithmetic and geometric sequences, sum series using sigma notation, determine whether infinite geometric series converge, count arrangements using permutations and combinations, expand binomials with the Binomial Theorem, and calculate probability for simple and compound events.
Learning Objectives
By the end of this unit, you will be able to:
Skills You Will Master
Real-World Connection
Sequences and series are the mathematics of accumulation. Compound interest is a geometric sequence — your savings grow by a constant ratio each period. Infinite geometric series explain why Zeno's paradoxes don't actually prevent motion. Counting principles and combinations are the foundation of combinatorics, which underlies cryptography, genetics, and tournament scheduling. The Binomial Theorem is used in statistics to model the number of successes in repeated trials. Probability governs insurance pricing, medical testing, and every game of chance. Unit 11 connects pure mathematics to the real world of data and decision-making.
Chapter Checklist
Recommended steps for completing each chapter
- Read the Workbook
- Complete the Independent Study
- Finish the Exit Ticket
- Take the Quiz
- Review the Answer Key
- Continue to the Next Chapter