1. Patterns and Sequences
1-7
Patterns and Sequences
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Determine 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, ___ 7 5 9 10 25

3. 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? 6 2 1 4 3 5

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

5. Vocabulary
perfect square
term
arithmetic sequence

6. Each month, Eva chooses 3 new DVDs from her DVD club. Eva’s DVDs Month 1 3 2 4
Position
Value
+ 3 6
+ 3 9
+ 3 12
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, …

7. A sequence is an ordered set of numbers
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.

8. Look for a relationship between the 1st term and the 2nd term
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

9. Additional Example 1A: Extending Arithmetic Sequences
Identify a pattern in each sequence and then find the missing terms.
48, 42, 36, 30, , , , . . .
–6 –6 –6 –6 –6 –6
Look for a pattern. A pattern is to subtract 6 from each term to get the next term.
30 – 6 = – 6 = – 6 = 12
So 24, 18, and 12 will be the next three terms.

10. Additional Example 1B: Extending Arithmetic Sequences
Position 1 2 3 4 5 6
Value of Term 9 22 35 48
+13
+13
+13
+13
+13
A pattern is to add 13 to each term to get the next term.
= = 74
So 61 and 74 will be the next terms in the arithmetic sequence.

11. Check It Out: Example 1A
Identify a pattern in each sequence and name the next three terms.
39, 34, 29, 24, , , , . . .
–5 –5 –5 –5 –5 –5
Look for a pattern. A pattern is to subtract 5 from each term to get the next term.
24 – 5 = – 5 = – 5 = 9
So 19, 14, and 9 will be the next three terms.

12. 1 2 3 4 5 6 7 16 25 34 Check It Out: Example 1B Position Value of Term+9 +9 +9 +9 +9
A pattern is to add 9 to each term to get the next term.
= = 52
So 43 and 52 will be the next terms in the arithmetic sequence.

13. Additional Example 2A: Completing Other Sequences
Identify a pattern in the sequence. Name the missing terms.
24, 34, 31, 41, 38, 48, , , ,…
+10 – – – –3
A pattern is to add 10 to one term and subtract 3 from the next.
48 – 3 = = – 3 = 52
So 45, 55, and 52 are the missing terms.

14. Additional Example 2B: Completing Other Sequences
Position 1 2 3 4 5 6 7 8
Value of Term 16 32
 4 ÷2
A pattern is to multiply one term by 4 and divide the next by 2.
8 ÷ 2 = 4 4  4 = ÷ 2 =  4 = 32
So 4 and 8 will be the missing terms in the sequence.

15. 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 = = 62
So 60 and 62 are the missing terms.

16. A pattern is to multiply one term by 6 and divide the next by 2.
Check It Out: Example 2B
Position 1 2 3 4 5 6 7 8
Value of Term 18 54
162
 6 ÷2
 6 ÷2
 6 ÷2
 6
A pattern is to multiply one term by 6 and divide the next by 2.
18 ÷ 2 = 9 9  6 = ÷ 2 =  6 = 162
So 9 and 27 will be the missing terms in the sequence.

17. 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.
, 500, , 125,…
4. 100, 50, 200, , 400, ,…
add 12; 60, 72, 84
subtract 4; 59, 55, 51
divide by 2; 250
divide by 2 then multiply by 4; 100, 200