Pre-Calculus Section 8.1A Sequences and Series

Chapter 8: Sequences, Series, and Probability Sequences and series describe algebraic patterns. We will learn how to use mathematical induction to prove formulas and how to use the Binomial Theorem. We will also study probability theory.

Sequences: - an ordered “list” of numbers - domain is the set of positive integers - use subscript notation: a n = 3n - 2

Infinite Sequence: - a function whose domain is the set of positive inters. The function values: a 1, a 2, a 3, a 4, …., a n, …… are the terms of the sequence ** If there are a set number of terms the sequence becomes a finite sequence.

Write the first four terms of each sequence. 1. a n = ½n + 5

Write the first four terms of each sequence. 2. a n = 3 + (- 1) n

Two Types of Sequences Arithmetic Sequence (common difference) a n = a 1 + (n-1)d a 1 : the 1 st term d :difference

Geometric Sequence (common ratio) a n = a 1 r n-1 a 1 : 1 st term r :common ratio

Types of Sequences Other There is no general formula Have to look for the pattern

Find the n th term of the Sequence: (write formula) 4.1, 3, 5, 7, ….

5.2, 5, 10, 17, …. Find the n th term of the Sequence: (write formula)

Find the n th term of the Sequence: (write formula)

Find the n th term of the Sequence: (write formula)

Find the n th term of the Sequence: (write formula)

Find the n th term of the Sequence: (write formula)

10.1, - 1, 1, - 1, 1, - 1, …. Find the n th term of the Sequence: (write formula)

Homework: Page Odd 33, Odd Quiz Wednesday: Sec 8-1