Chapter 4 Sequences Series Ch 4 Sequences Series

Chapter 4 Sequences & Series Ch. 4 : Sequences & Series 1

This chapter consists of 3 sections as follows: 4. 1 Sequences & Series 4. 2 Arithmetic Sequences & Series 4. 3 Geometric Sequences & Series Ch. 4 : Sequences & Series 2

4. 1 Sequences & Series Ch. 4 : Sequences & Series 3

I. Sequences Ch. 4 : Sequences & Series 4

Sequences A finite sequence is a function that has a set of natural numbers of form as its domain. An infinite has the set of natural numbers as its domain. For example Ch. 4 : Sequences & Series 5

Example 1 Write the first five terms for Ch. 4 : Sequences & Series 6

Solution: is called the general term of the sequence Ch. 4 : Sequences & Series 7

Ch. 4 : Sequences & Series 8

Class Work Write the first five terms of each sequence Ch. 4 : Sequences & Series 9

Exercise 11. 1 page 936 -937 24 In Exercises 1 to 24, find the first three terms for the given sequences. Ch. 4 : Sequences & Series 10

II. Series Ch. 4 : Sequences & Series 11

Series A finite series is an expression of form and an infinite is an expression of form Ch. 4 : Sequences & Series 12

Example 2 Evaluate the series Solution: Ch. 4 : Sequences & Series 13

Class Work Evaluate each series Ch. 4 : Sequences & Series 14

3. Arithmetic sequences and series Ch. 4 : Sequences & Series 15

I. Arithmetic Sequences Ch. 4 : Sequences & Series 16

A sequence in which each term after the first is obtained by adding a fixed number to the previous term is an arithmetic sequence. The fixed number is called the common difference “d”. The sequence is an arithmetic sequence, since each term after first is obtained by adding 4 to the previous term The common difference Ch. 4 : Sequences & Series 17

Example 3 Find the common difference, d, for Solution Example 4 Write the first five terms for each arithmetic sequence Solution Ch. 4 : Sequences & Series 18

The nth term of an arithmetic sequence Example 4 Find and for the arithmetic sequence Solution Ch. 4 : Sequences & Series 19

Exercise 11. 2 page 943 25 In Exercises 1 to 14 , find the ninth, twenty-fourth , and nth terms of the arithmetic sequence. 3. 6, 4, 2, . . . 5. -8, -5, -2, . . . 7. 1, 4, 7 , . . . In Exercises 19 to 32 , find the sum of the following arithmetic sequence. Ch. 4 : Sequences & Series 20

II. Arithmetic Series Ch. 4 : Sequences & Series 21

If an arithmetic sequence has first term and common difference , the sum of the first n terms is given by or Ch. 4 : Sequences & Series 22

Example 5 a) Evaluate for the arithmetic sequence b) The sum of the first 17 terms of arithmetic sequence is 187. If find and. Solution Solve these two equation to get Ch. 4 : Sequences & Series and 23

Class Work Evaluate Ch. 4 : Sequences & Series 24

4. Geometric Sequences and Series Ch. 4 : Sequences & Series 25

I. Geometric Sequences Ch. 4 : Sequences & Series 26

A geometric sequence (or geometric progression) is a sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero real number. The fixed real number is called the common ratio “r”. The sequence is a geometric sequence, since each term after first is obtained by multiplying 2 to the preceding term The common ratio Ch. 4 : Sequences & Series 27

The nth term of a geometric sequence Example 6 Find and for the geometric sequence Solution Ch. 4 : Sequences & Series 28

Class Work Find and for the geometric sequence having and. Ch. 4 : Sequences & Series 29

II. Geometric Series Ch. 4 : Sequences & Series 30

1. Partial sum (the sum of the first n terms) 2. Infinite sum (the sum of an infinite terms) Ch. 4 : Sequences & Series 31

Example 7 Find: Solution Ch. 4 : Sequences & Series 32

Class Work Find each sum Ch. 4 : Sequences & Series 33

Exercise 11. 3 page 954 26 In Exercises , find the sum of the finite geometric series. In Exercises, find the sum of the infinite geometric series. Ch. 4 : Sequences & Series 34