lesson 11.1

Lesson 11.1

Sequences and Series

Warm Up:

Comprehension Quiz:Read page 690…1) Who were Titius and Bode?

Close your books

2) What does their sequence model?German Astronomers

The distances between the sun and the planets

3) What did they find at the distance corresponding to the fifth bode number?

Ceres

4) The asteroid belt containing Ceres lies between which 2 planets?

Mars and Jupiter

By reading page 691, define the following terms:

Vocabulary:Sequence:

Terms:

Infinite Sequence:

Ellipsis:

Finite Sequence:

Explicit Formula:

An ordered list of numbers, called terms

The numbers in a sequence

A sequence that continues without end

Three dots, used to indicate an infinite sequence

A sequence that has a last term

A formula that defines the nth term, or general term, of a sequence

n 1 2 3 4 5 6

tn 1 7 17 31 49 71

The first six terms are: 1, 7, 17, 31, 49, and 71

TRY THIS, page 691

1 11 and 3 1, where 2n nt t t n

13 1n nt t

2 13 1 3(1) 1 2t t

3 23 1 3(2) 1 5t t

4 33 1 3(5) 1 14t t

5 43 1 3(14) 1 41t t

6 53 1 3(41) 1 122t t

1 1t

The first six terms are 1, 2, 5, 14, 41, 122

Planet Bode Number Distance from the planet to Sun

5th: Ceres

6th: Jupiter

7th: Saturn

8th: Uranus

By reading page 693, define the following terms:

Vocabulary:Series:

Summation notation:

Sigma:

An expression that indicates the sum of terms of a sequence

A way to express a series in abbreviated form, using the Greek letter sigma

5

1

2n

n Explicit formula for the general

term of the related sequence

Values of n from 1 to 5 are called the index

TRY THIS, page 693

5

1

a. 4k

k

4

1

1b. 2 k

k

4 8 12 16 2060

1 1 2 3 42

1 1025

Homework:

Practice 11.1