1. 4.7: Arithmetic sequences
I can write a recursive formulas given a sequence.
Day 1

2. Describe a pattern in each sequence. Then find the next two terms.
7, 10, 13, 16 ___, ___, … 19 22
Add 3
3, 6, 12, ___, ___, … 24 48
Mult by 2
99, 88, 77, ___, ___, … 66 55
Subtract 11

3. Ex: 3, 5, 7, 9, … 2 Common difference for the above sequence:
Arithmetic sequences:
In an arithmetic sequence: The difference between each consecutive term is constant. This difference is called the common difference (d).
Ex: , 5, 7, 9, … 2
Common difference for the above sequence:

4. If there is a common difference, what is it?
7, 10, 13, 16 ___, ___, … 19 22 3
3, 6, 12, ___, ___, … 24 48
Common difference:
There isn’t one.
99, 88, 77, ___, ___, … 66 55
Common difference:
-11

5. Is the following sequence arithmetic? If it is, describe the pattern.no
Why not: I started with 5 and then multiplied by 2 each time.
b. 5, 8, 11, 14…
I started with 5 and then added 3 each time.
yes
c. 20, 5, -10, -25, …
I started with 20 and then added
-15 each time.
yes

6. General term or nth term A(n-1)= Previous term
An ordered list of numbers defined by a starting value (number) and a rule to find the general term.
Recursive Formula:
A(1) =
first term
A(n) =
General term or nth term
A(n-1)=
Previous term
Given the following recursive formula, find the first 4 terms.
A(1) = 20
20,
26,
32, 38
A(n) =
A(n-1) + 6
1st term 2nd term 3rd term 4th term
Think: previous term + 6
Given the following recursive formula, find the first 4 terms.
A(1)=
-18
-18,
-21,
-24,
-27,
1st term 2nd term 3rd term 4th term
A(n) =
A(n-1) - 3
Think: previous term -3

7. Write a recursive formula for each sequence.
7, 10, 13, 16, … 7
Recursive rule: 7
A(1) = 7
A(n) = A(n-1) + 3
A(1) =
A(1) = ____ +3
A(n) = A(n-1)
A(n) = A(n-1) + d 3
3, 9,15, 21,…
97, 87, 77, 67 …
A(1) = 3
A(n) = A(n-1) + 6 3
A(1) =
A(1) = 97
+ 6
A(n) = A(n-1)
A(n) = A(n-1)
- 10
Homework: pg 279: 9-35