4.7: Arithmetic sequences

I can write a recursive formulas given a sequence.

Day 1

7, 10, 13, 16 ___, ___, …

3, 6, 12, ___, ___, …

19 22

24 48

Describe a pattern in each sequence. Then find the next two terms.

99, 88, 77, ___, ___, …66 55

Add 3

Mult by 2

Subtract 11

Arithmetic sequences:

In an arithmetic sequence: The difference between each consecutive term is constant. This difference is called the common difference (d).

Ex: 3, 5, 7, 9, …

Common difference for the above sequence: 2

7, 10, 13, 16 ___, ___, …

3, 6, 12, ___, ___, …

19 22

24 48

If there is a common difference, what is it?

99, 88, 77, ___, ___, …66 55

Common difference:

3

Common difference:

There isn’t one.

Common difference:

-11

Is the following sequence arithmetic? If it is, describe the pattern.

a. 5, 10, 20, 40, …

b. 5, 8, 11, 14…

c. 20, 5, -10, -25, …

no Why not: I started with 5 and then multiplied by 2 each time.

yes I started with 5 and then added 3 each time.

yesI started with 20 and then added

-15 each time.

Recursive Formula: An ordered list of numbers defined by a starting value (number) and a rule to find the general term.

A(1) = A(n) = General term or nth termfirst term

A(n-1)= Previous term

Given the following recursive formula, find the first 4 terms.

A(1) = 20

A(n) = A(n-1) + 6 20, 26, 32, 38

Given the following recursive formula, find the first 4 terms.

A(1)= -18

A(n) = A(n-1) - 3

-18, -21, -24, -27,

1st term 2nd term 3rd term 4th term

1st term 2nd term 3rd term 4th term

Think: previous term + 6

Think: previous term -3

Write a recursive formula for each sequence. (always has two parts)

7, 10, 13, 16, …

A(1) = ______

A(n) = A(n-1)_____

A(1) = ____

A(n) = A(n-1)

Recursive rule:

7

7

+3

A(1) = 7A(n) = A(n-1) + 3 3, 9,15, 21,…A(1) =

A(n) = A(n-1)

33

+ 6A(1) = 3A(n) = A(n-1) + 6

97, 87, 77, 67 …

A(1) = 97

- 10

Homework: pg 279: 9-35

A(n) = A(n-1) + d