6th Grade Math Textbook, Progress

Algebraic Patterns

14-9

Find the next two terms in each sequence.

Describe the pattern.

1. 3, 9, 27, 81, ... 2. 10, 8, 6, 4, ... 3. 21, 25, 29, 33, ...


2. 1 ,
   ^12
   ,
   ^14
   ,
   ^18
   ,... 5. 1 ,
   ^12
   ,
   ^13
   ,
   ^14
   ,... 6. 1 ,
   ^14
   ,
   ^19
   , ,...


3. 2.5, 3, 3.5, 4, ... 8. 0.1, 0.8, 1.5, 2.2, ... 9. 61, 54.5, 48, 41.5, ...


4. 200, 100, 50, 25,... 11. 81, 27, 9, 3,... 12. 0.1, 0.01, 0.001. 0.0001...

1

16

A sequence is an ordered set of numbers that follow a pattern.

Each number in a sequence is called a term. Write ... to show

that a sequence continues indefinitely.

Study these sequences.

A. 2, 4, 6, 8, 10, 12, ...

Start at 2. Add 2 repeatedly.

B. 4, 8, 16, 32, 64, 128, ...

Start at 4. Multiply by 2 repeatedly.

C. 1, 2, 4, 5, 10, 11, 22, 23, 46, ...

Start at 1. Add 1, then double; add 1, then double; and so on.

For each sequence above, you found the next term by first finding a pattern,

and then using the pattern to make a conjecture about the next term.

Triangular and square numbers are sequences of whole numbers.

Each number can be represented by an arrangement of dots.

A. The first two triangular numbers

are 1 and 3. What are the next

two triangular numbers?

B. The first two square numbers are

1 and 4. What are the next two

square numbers?

1 3 6 10

1 4 9 16

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