6th Grade Math Textbook, Fundamentals

Lesson 13-2 for exercise sets. &KDSWHU 

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Identify and extend each pattern by 3 terms.

1. , 1, 3, 4, 6,... 2.1, 8, 27, 64,... 3.4, 3, 0, 1, 0, 1, ...

4.Identify the sequence represented by the visual pattern of squares above.

5.Discuss and Write Explain why 3^1 , 3^2 , 3^3 , 3^4 , 3^5 ,... is a geometric sequence.

1

2

1

2

1

2

1

2

1

2

What is the 11th term in the sequence: 1, 4, 9, 16, 25,...?

Relate each term to its position in the sequence using a table.

The value of each term is the square of its position in the sequence.

So the 11th term is (11)^2 121.

Position 123 4 5

Term 1491625

1

The sequence of factorials is 1, 2, 6, 24, 120,...

What is the next term in the sequence?

Relate each term to its position in the sequence using a table.

The value of each term is the factorial of its position in the sequence.

So the next term is 6! 720.

Position 123 4 5

Term 1 2 6 24 120

2

The repeating step in a visual pattern is called an.

What is the next term in this visual pattern?

Pattern rule: Start with 1 square, and then divide

each square in each succeeding term

into 4 squares.

The iteration is the division of each square into 4 squares.

The next term in the pattern is:

iteration

Think

The position number

squared equals the term.

12  1

22  4

32 9, and so on

Think

The factorial of the position

number equals the term.

1!  1

2!  2

3! 6, and so on