Section 11-1

Sequences and Series

Definitions

A sequence is a set of numbers in a specific order

2, 7, 12, …

Definitions

An arithmetic sequence is a sequence in which each term is equal to the sum of the preceding term and the common difference.

a1, a1 d a1 2d a1 3d ...

Definitions

The difference between successive terms of an arithmetic sequence is a constant called the common difference d

1. What is the common difference?

3 6 9 12 15 18 ...

2. Find the next three terms for the sequence

12, 1, 10...

3. Find the next three terms for the sequence

r 4, r 1, r 2 ...

Definitions

An arithmetic series is the sum of the terms of an arithmetic sequence.

Definitions

A geometric sequence is one in which each term after the first is a product of the proceeding term and a common ratio r.

a, ar, ar2 ... arn

5. What is the common ratio for 13, 91, 637 ?

Definitions Limit of a function at infinity

The limit of a function is the limit as x approaches positive or negative infinity.

It means that x either grows without bound positively (positive infinity) or grows without bound negatively (negative infinity).

Definitions

A sequence or series that is getting infinitely large is said to diverge.

Definitions

A sequence or series that is getting infinitely small is said to converge.

Definitions

The nth term is a general formula for the sum of the terms of a sequence or series

6. Find the limit of the sequence then determine if it converges or diverges

3

3

3

6...,

81

45,

24

20,3

7

n

nn

7. n

n

n 3

64lim 2

8. Write 0.4545… as a fraction

9. Write 7.259259… as a fraction

Assignment

Practice 11-1