6th Grade Math Textbook, Progress

Patterns: Sequences

Find the rule.

Then use it to find the next term.

Label the sequence arithmeticor geometric.

0 1. 10, 18, 26, 34, 42,... 0 2. 5, 20, 80, 320, 1280,...

0 3. 106, 81, 56, 31,... 0 4. 2.5, 5, 7.5, 10,...

0 5. 0.4, 1.2, 3.6, 10.8,... 0 6. 176.5, 17.65, 1.765, 0.1765,...

0 7. 0.125, 0.25, 0.5, 1,... 0 8. 2, 0.4, 0.08, 0.016,...

A sequence is a set of numbers in a certain order, usually by a pattern.

Each number is called a term. A term can be found by using a pattern rule.

What is the rule for the sequence?

What is the next term in the sequence?

1, 5, 9, 13, 17,...


 4 
 4 
 4 
 4

Rule:Start with 1 and add 4 repeatedly.

Next term: 17 
 4 , or 21

What is the rule for the sequence?

What is the next term in the sequence?

2.1, 4.2, 8.4, 16.8,...

 2  2  2

Rule:Start with 2.1 and multiply by 2

repeatedly.

Next term:16.8  2 , or 33.6

This is an arithmetic sequence

because each new term is found

by adding or subtracting a fixed

number to the previous term.

This is a geometric sequence

because each new term is found

by multiplying or dividing by a

fixed number.

Use the sequence 1, 3, 5, 7,... for problems 9 and 10.

0 9. What is the sum of the first 2 terms? the first 3

terms? the first 4 terms? the first 5 terms?

10. Look at the sums you found. What pattern do you see?
    Use the pattern to predict the sum of the first 8
    terms in the sequence. Check your prediction.

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