Analyzing Number Patterns

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Presentation transcript:

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

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

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

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

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

Arithmetic Sequence Each term of an arithmetic sequence is the output of a function Each term is labeled with a term number Term Number 1 2 3 4 Term 7 11 15 19

Arithemetic Sequence Use the common difference of the terms to write a rule for the sequence. 7, 11, 15, 19 Common difference is 4

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

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 = 2 + 4*6= 2 + 24= 26 A(6) = 2 + (6-1)*6= 2 + 5*6 = 2 + 30= 32

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)

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= 2 + 33= 35 A(20)= 2 + (20-1)*3= 2+ 19*3= 2+ 57 = 59 A( 100) = 2 + (100-1)*3 = 2+ 99*3 = 2+297 = 299

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

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

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,. . . . .

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