Unit 11

Sequences, Series, and Probability

Explore arithmetic and geometric sequences, series, the Binomial Theorem, permutations, combinations, and probability.

Unit 11 · 9 pages

Lessons

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 11 Sequences, Probability & Counting Theory.

Write sequences using explicit and recursive formulas; use sigma notation for series.

Identify arithmetic sequences, write explicit formulas, and find partial sums Sₙ = n(a₁ + aₙ)/2.

Identify geometric sequences, write aₙ = a₁·rⁿ⁻¹, and find finite and infinite series sums.

Evaluate series using sigma notation; apply summation formulas and determine convergence.

Apply the Fundamental Counting Principle, permutations P(n,r), and combinations C(n,r).

Expand (a + b)ⁿ using binomial coefficients and Pascal's Triangle; find specific terms.

Calculate theoretical probability; apply addition and multiplication rules; use combinations for probability.

Consolidate your understanding of sequences, series, the Binomial Theorem, counting principles, and probability.