Unit 3 · 8 lessons
Discrete Functions
Sequences, series, Pascal's triangle, and the financial math (interest and annuities) that sequences make possible.
- 93 practice questions
- 70 flashcards
- 2 interactive lessons
Lessons
- 1Sequences as Discrete FunctionsA sequence is a function whose domain is the natural numbers. Learn term notation, the difference between explicit and recursive formulas, and how to responsibly find a pattern.11 questions
- 2Arithmetic SequencesSequences that grow (or shrink) by the same fixed amount every step. Master the common difference, the formula , and solving for any missing piece.Interactive11 questions
- 3Geometric SequencesSequences that grow (or shrink) by the same fixed FACTOR every step — the mathematical model behind compound interest, population growth, and radioactive decay.11 questions
- 4Arithmetic SeriesA series is the SUM of a sequence's terms. Learn both sum formulas for arithmetic sequences and the famous Gauss pairing trick that derives them.12 questions
- 5Geometric SeriesSumming a geometric sequence needs a different trick from arithmetic series — a shift-and-subtract derivation that produces a clean formula.12 questions
- 6Pascal's Triangle and the Binomial TheoremPascal's triangle is packed with patterns, and its rows are exactly the coefficients you need to expand without multiplying it out by hand.12 questions
- 7Simple and Compound InterestSimple interest grows in a straight line (arithmetic); compound interest grows geometrically. Learn both formulas, compounding periods, and running the compound formula backward to find present value.12 questions
- 8Simple AnnuitiesAn annuity is a series of equal, regular payments — think loan payments or automatic savings deposits. Learn the future value and present value formulas for ordinary simple annuities.Interactive12 questions