6th Grade Math Textbook, Fundamentals

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Lesson 13-1 for exercise sets. &KDSWHU 

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Describe each sequence as arithmetic, geometric, or neither.

If the sequence is arithmetic or geometric, determine its 7th term.

1.10, 3, 4, 11,... 2.625, 125, 25, 5, ... 3.1, 1, 2, 3, 5,... 4.7, 1, 3, 2, 10,...

Find the missing term for each sequence.

5.1, 1.1, ?, 1.331,... 6. , , , ?, 3,... 7.?, 11 , 8 , 5 ,...

8.Discuss and Write Describe an arithmetic sequence and a geometric sequence.

256

27

3

5

3

10

9

10

16

3

64

9

Find the missing term for the arithmetic sequence. 111, ?, 84.6, 71.4, 58.2,...

• Find the constant difference. 71.4 84.6 13.2


• Then add the constant difference to 111. 111 (13.2) 97.8

1

The constant ratio of a

geometric sequence can

be a positive or negative

number.

Find the missing term for the geometric sequence. 512 , 64, ?, 1, , ,...

• Find the constant ratio. 


• Then multiply 64 by the constant ratio. 64 •^18  8

1

8

64

512

1

8

1

(^264)

Some sequences are neither arithmetic nor geometric, and some are both. For

the sequence 6, 5, 10, 9, 18, 17, 34,..., there is neither a constant difference nor

a constant ratio. The sequence 1, 1, 1, 1, 1,... is both arithmetic and geometric,

since the rules add 0 to each term andmultiply each term by 1both apply.

You can find missing terms in an arithmetic sequence or geometric sequence.

A is a sequence of numbers in which each term

is found by multiplying the preceding term by a fixed number, called

the. In order to determine if a sequence is a geometric

sequence, examine the consecutive terms. If all consecutive terms

have a constant ratio, the sequence is geometric.

Find the next three terms in the sequence: 3, 12, 48, 192,...

  The constant ratio is or 4.

The ratio is always 4, so the sequence is geometric.

The pattern rule is: Start at 3, and multiply by 4 repeatedly.

So to find the next three terms in the pattern, multiply each succeeding term by 4.

3, 12, 48, 192, 768, 3072, 12,288

4

1

4

1

192

48

48

12

12

3

constant ratio

geometric sequence

Think

192(4)  768

768(4)  3072

3072(4) 12,288