DAY 30 AGENDA: Quiz Tues

Unit #4: Sequences & Series Accel Precalc Unit #4: Sequences & Series Lesson #1: Sequences and Series EQ: How do you evaluate a finite series?

New Terms: Mathematical Sequence --- function notation made up of terms using subscript notation a1, a2, a3, a4, …, an --- sequence of values from 1 to  Infinite Sequence Finite Sequence --- sequence for first n positive integers

Explicit --- allows you to find ANY term in the sequence RECALL: What is the difference between the recursive and the explicit formula for a sequence? Explicit --- allows you to find ANY term in the sequence Recursive --- allows you to find the NEXT term only

Are these sequence formulas explicit or recursive? Explicit --- can obtain any term in the sequence

Ex. Find the first 4 terms of the following sequence. a4 = 4(32) a2 = 4(2) a3 = 4(8) Is this sequence formula explicit or recursive? Recursive --- can only obtain next term from previous term

Recall: What does the notation n! mean? Factorial --- (n)(n – 1)(n – 2)… (2)(1) What does 0! = ? 1

Ex. Find the first four terms in the sequence begin with n = 0. Ex. Evaluate. 28 2 n

Assignment: Textbook p. 625 Odds #1 – 21, 29 - 33

Ex. Evaluate the following.

Assignment: Textbook p. 625 Odds #69 - 89

Ex. Express each of the following using summation notation. 1. 1 + 2 + 3 + … + 20 i 1 2 3 4 … 20 f(i) 1 2 3 4 … 20 f  i 20

Try these on your own:

Series --- sum of the terms of a sequence from k = 1 to k = i a1 + a2 + a3 + a4 + … + ai + … Infinite Series --- sum of all terms of the infinite sequence

Finite Series or nth Partial Sum --- sum of the first n terms of a sequence Ex. Find the indicated partial sum of the series.

Assignment: p. 625 ODDS #1 – 21, 29 – 33, 51 - 57, 69 – 89, 105, 107