Course 1

1-7 Patterns and Sequences1-7 Patterns and Sequences

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

1-7 Patterns and Sequences

Warm UpDetermine what could come next.

1. 3, 4, 5, 6, ___2. 10, 9, 8, 7, 6, ___3. 1, 3, 5, 7, ___4. 2, 4, 6, 8, ___5. 5, 10, 15, 20, ___

7591025

Course 1

1-7 Patterns and Sequences

Problem of the Day

How can you place the numbers 1 through 6 in the circles so that the sums along each side are equal?

1

534

26

Course 1

1-7 Patterns and Sequences

Learn to find patterns and to recognize, describe, and extend patterns in sequences.

Course 1

1-7 Patterns and Sequences

Vocabulary

perfect square

term

arithmetic sequence

Course 1

1-7 Patterns and Sequences

Each month, Eva chooses 3 new DVDs from her DVD club.

Eva’s DVDs

Month DVDs

1 3

2

3

4

ValuePosition

The number of DVDs Eva has after each month shows a pattern: Add 3. This pattern can be written as a sequence.

3, 6, 9, 12, 15, 18, …

+ 3

+ 312

9+ 36

Course 1

1-7 Patterns and Sequences

A sequence is an ordered set of numbers. Each number in the sequence is called a term. In this sequence, the first term is 3, the second term is 6, and the third term is 9.

When the terms of a sequence change by the same amount each time, the sequence is an arithmetic sequence.

Course 1

1-7 Patterns and Sequences

Look for a relationship between the 1st term and the 2nd term. Check if this relationship works between the 2nd term and the 3rd term, and so on.

Helpful Hint

Course 1

1-7 Patterns and Sequences

Additional Example 1A: Extending Arithmetic Sequences

Identify a pattern in each sequence and then find the missing terms.

48, 42, 36, 30, , , , . . .

Look for a pattern. A pattern is to subtract 6 from each term to get the next term.

30 – 6 = 24 24 – 6 = 18 18 – 6 = 12

So 24, 18, and 12 will be the next three terms.

–6 –6 –6 –6 –6 –6

Course 1

1-7 Patterns and Sequences

Additional Example 1B: Extending Arithmetic Sequences

A pattern is to add 13 to each term to get the next term.

48 + 13 = 61 61 + 13 = 74

So 61 and 74 will be the next terms in the arithmetic sequence.

Position 1 2 3 4 5 6Value of Term 9 22 35 48

+13 +13 +13 +13+13

Course 1

1-7 Patterns and Sequences

Check It Out: Example 1A

Identify a pattern in each sequence and name the next three terms.

39, 34, 29, 24, , , , . . .

Look for a pattern. A pattern is to subtract 5 from each term to get the next term.

24 – 5 = 19 19 – 5 = 14 14 – 5 = 9

So 19, 14, and 9 will be the next three terms.

–5 –5 –5 –5 –5 –5

Course 1

1-7 Patterns and Sequences

Check It Out: Example 1B

A pattern is to add 9 to each term to get the next term.

34 + 9 = 43 43 + 9 = 52

So 43 and 52 will be the next terms in the arithmetic sequence.

Position 1 2 3 4 5 6Value of Term 7 16 25 34

+9 +9 +9 +9+9

Course 1

1-7 Patterns and Sequences

Additional Example 2A: Completing Other Sequences

Identify a pattern in the sequence. Name the missing terms.

24, 34, 31, 41, 38, 48, , , ,…

A pattern is to add 10 to one term and subtract 3 from the next.

48 – 3 = 45 45 + 10 = 55 55 – 3 = 52

So 45, 55, and 52 are the missing terms.

+10 –3 +10 –3 +10 –3 +10 –3

Course 1

1-7 Patterns and Sequences

Additional Example 2B: Completing Other Sequences

A pattern is to multiply one term by 4 and divide the next by 2.

8 ÷ 2 = 4 4 4 = 16 16 ÷ 2 = 8 8 4 = 32

So 4 and 8 will be the missing terms in the sequence.

Position 1 2 3 4 5 6 7 8

Value of Term 1 4 2 8 16 32

4 ÷2 4 4÷2 ÷2 4

Course 1

1-7 Patterns and Sequences

Check It Out: Example 2A

Identify a pattern in each sequence and name the missing terms.

6, 12, 14, 28 , 30, , ,. . .

A pattern is to multiply one term by 2 and add 2 from the next.

30 2 = 60 60 + 2 = 62

So 60 and 62 are the missing terms.

2 + 2 2 + 2 2 + 2

Course 1

1-7 Patterns and Sequences

Check It Out: Example 2B

A pattern is to multiply one term by 6 and divide the next by 2.

18 ÷ 2 = 9 9 6 = 54 54 ÷ 2 = 27 27 6 = 162

So 9 and 27 will be the missing terms in the sequence.

6

÷2 6

6

÷2

Position 1 2 3 4 5 6 7 8

Value of Term 1 6 3 18 54 162

÷2 6

Course 1

1-7 Patterns and Sequences

Lesson Quiz

Identify a pattern in each sequence, and then find the missing terms.

1. 12, 24, 36, 48, , , , …

2. 75, 71, 67, 63, , , ,…

Identify a pattern in each sequence. Name

the missing terms.

3. 1000, 500, , 125,…

4. 100, 50, 200, , 400, ,…

subtract 4; 59, 55, 51

add 12; 60, 72, 84

divide by 2; 250

divide by 2 then multiply by 4; 100, 200