Sequences5.2

Arithmetic Sequences

Numbers Words

Continue each sequence.

1,3,5,7,__,__,...1,1.5,2,__,__,__,..

Describe each sequence.

Add __ to the previous term.Add ___ to the previous term.

Pg. 357

Real-World LinkHorseback Riding: The number of students who went on each horseback riding trip is show. Do the numbers represent the terms of an arithmetic sequence? Explain.Trip 1 2 3 4 5

Number of Students

15 16 18 21 25

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Vocabulary

arithmetic sequence - a list of numbers in which the next term is found by _______ the same number to the previous term.

geometric sequence - a list of numbers in which the next term is found by ________ the previous term by the same number to get the next term.

Describe and Extend Sequences

• In an ___________, the terms can be whole numbers, fractions, or decimals.

• Examples on pg. 358

Write an Algebraic Expression

• In a _________, each term has a specific position within the sequence.

• Consider the sequence 2, 4, 6, 8…

2, 4, 6, 8, …1st position ___ position

__ position ___ position

Arithmetic Sequences

2, 5, 8, 11, 14, . . . .

+3 +3 +3 +3

the same number was added

common difference = 3

n + 3

1, 8, 15, 22, 29, . . . .

+7 +7 +7 +7

the same number was added

common difference = 7

n + 7

Geometric Sequences

2, 6, 18, 54, . . . .

•3 •3 •3

multiplied by the same number

common ratio = 3

3n

1, 5, 25, 125, . . . .

•5 •5 •5

multiplied by the same number

common ratio = 5

5n

Geometric Sequences

Find the 7th term in the sequence.

89, 86, 83, 80. . .

-3 -3 -3

77 74 71

2, 4, 8, 16. . .

•2 •2 •2

32 64128

n-3

2n

Arithmetic or Geometric Sequence?Then find the next 3 terms & the algebraic expression.

7, 12, 17, 22. . .

+5 +5 +5

27 32 37

64, 32, 16, 8. . .

•0.5 •0.5 •0.5

4 2 1

÷2 ÷2 ÷2

n+5

0.5n

Classwork Practice

Classwork PracticeIdentify each sequence as arithmetic or

geometric, then write a variable expression to describe it.

1. 2, 4, 6, 8, ....

2. 6, 12, 24, 48, ....

4. 4, 7, 10, 13, ....

3. 4, 4, 4, 4, 4, ....

5. 1, 7, 13, 19, ....

6. 2, 4, 8, 16, ....

7. 11, 22, 33, 44, ....

8. 24, 12, 6, 3, ....

9. 21, 18, 15, 12, ....

10. 2, 8, 32, 128, ....