4.6 Sequences and Series

4.6 Sequences and Series

An Arithmetic sequence is an ordered list of numbers where you add the same number.

example 5, 10, 15, 20, ... a_n

5 is first position

10 is second position

n is nth position

Example 1. Write the next three terms.

First term is 2

Common difference is 5

• 7

• 12

• 15

Example 2. Write the next three terms.

First term is 10

Common difference is -2

• 8

• 6

• 4

Find the common difference of

13, 18, 23, 28, ....

• 5

• we add five

Find the common difference of

50, 40, 30, 20, ....

• -10

• subtract 10

• need negative / subtraction sign

Write the next 3 numbers of the sequence.

14, 16, 18, 20, ...

• we add 2

• 22

• 24

• 26

Write the next 3 numbers of the sequence.

32, 27, 22, 17, ...

• we subtract 5

• 12

• 7

• 2

Arithemetic means add or subtract.

Cannot multiply or divide or be random.

Multiple Choice

Is it a sequence?

2, 4, 8, 16

• Yes

• No

Multiple Choice

Is it a sequence?

125, 25, 5, 1, ...

• Yes

• No

Multiple Choice

Is it a sequence?

1, 2, 4, 7, ....

• Yes

• No

Graph the sequence 1, 3, 5, 7

x is the position

y is the number given.

1, 1

2, 3

3, 5

4, 7