1. Analyzing Number Patterns
Algebra Concept
Patterned after analyzing the ancient teachings of the great one, Mr. Peter Richard

2. Inductive Reasoning
Making a conjecture based on what you’ve already seen
Conjecture an educated guess or conclusion

3. EXAMPLES A) 2, 6, 10, 14, …… B) 2, 4, 8, 16, …… C) 2, -4, 8, -16, ……
B) 2, , , , ……
* * * *2
C) 2, , 8, , ……
* * * *-2

4. Sequence Number Pattern
2, 4, 6, 8, 10
Term each number in a sequence 2 4
Arithmetic Sequence kind of sequence formed by adding a fixed number to each previous term
Common Difference the fixed number

5. Finding the Common Difference
A) -7, -3, 1, 5
The common difference is 4
B) 17, 13, 9, 5
The common difference is -4

6. Arithmetic Sequence
Each term of an arithmetic sequence is the output of a function
Each term is labeled with a term number
Term Number
Term

7. Arithemetic Sequence
Use the common difference of the terms to write a rule for the sequence.
7, , ,
Common difference is 4

8. Arithmetic Sequence RULE A(n) = a + (n -1) * d nth first term common
term term number difference

9. Arithmetic Sequence Write a rule for the sequence 2, 8, 14, 20 A(1)= 2
2, 8, 14, 20
A(1)= 2
A( n) = 2 + (n-1)*6
Check it!
Find the next 2 terms of the pattern.
26, 32
Find the next 2 term of the arithmetic sequence.
A(5) = 2 + (5-1)*6 = *6= = 26
A(6) = 2 + (6-1)*6= *6 = = 32

10. Arithmetic Sequence 8, 6, 4, 2 A(1) = 8 A(n) = 8 + (n-1)* -2
8, 6, 4, 2
A(1) = 8
A(n) = 8 + (n-1)* -2
Once a rule is written, you can find the value of ANY term!
A(5) = 8 + (5-1) *-2 =
8+ 4*(-2) =
8+ (-8)

11. Find a value
Given a arithmetic sequence, find the 9th , 12th , 20th , and 100th values
A(n) = 2 + (n-1)* 3
A(9) = 2 + (9-1) *3 = 2+ 8*3= 2+ 24= 26
A(12)= 2 + (12-1)*3= 2+ 11*3= = 35
A(20)= 2 + (20-1)*3= 2+ 19*3= = 59
A( 100) = 2 + (100-1)*3 = 2+ 99*3 = = 299

12. Work it out!
Find the 4th , 6th , and 10th terms
A(n) = 3 + (n-1) * -3

13. Homework Pg 270 1-11 odd, 13, 14, 18, 20, 23-27 odd 13 problems
Due next class!

14. Describe a pattern for each sequence.
3, 8, 18,
1, 2, 4, 8, 16,
4, 10, 16, 22,
2, 6, 18, 54,
95, 93, 90, 86,

16. Answers 5 more than previous number 23, 28, 33,
Twice the previous number 32, 64, 128,
6 more than the previous number 28,34, 40
3 times previous number 162,486, 1458