Subjects: Sequences and Series

Identifies finite and infinite sequences, the terms of a sequence given a function that describes it, and functions that describe simple sequences. Provides an observation of the Fibonacci sequence in nature.

Addresses how to write the terms of a sequence, given its recursive definition, and the converse: how to define a sequence recursively, given its terms. Shows how a computer program performs the calculations indicated by a recursive definition.

Emphasis is placed on understanding the patterns in arithmetic sequences and the general term formula is manipulated to solve for a, n, tn, and d. A system of equations is used to solve an arithmetic means problem.

Students learn to identify what makes a sequence geometric, and using the principles behind its definition, derive its general term. Examples of geometric sequences found in music are explored.

Develops both forms of the sum formula used for arithmetic series questions. Manipulation of the formula demonstrates how to solve for a variety of unknowns. Demonstrates several different problem solving approaches using an open-ended question.

Examines the information explosion, animal population and aspects of the Orb spider web as examples of geometric series. Presents the general term formula for geometric series and are shows how to manipulate the formula to solve a variety of problems.

“Why is sigma notation useful?” and “Where is it actually used?” are questions answered in this program. Shows how calculators use sigma notation to determine trigonometric ratios and examines the various patterns present in Pascal’s triangle.

This review of arithmetic and geometric sequences and series uses several common-sense approaches and formula manipulation to work with the patterns and relationships in a string of numbers.