Extend a Pattern: Mini-Lesson Review

Use a Rule to Extend a Pattern

Pattern rules can use one or more mathematical operations to describe the relationship between consecutive numbers in a list of numbers, or sequence. Knowing the pattern rule will help you extend the pattern. To extend the pattern means to use the pattern rule to write the numbers that would come next in the sequence.

Try to see the difference between consecutive numbers. It will help you understand the relationship between the numbers.

Find the next two numbers in the following sequence:

3, 6, 9, 12, . . .

First, figure out the pattern rule. The numbers are increasing, so the rule likely involves addition or multiplication.

• Look at the first two terms, 3 and 6. What operation could you perform on 3 to get 6?
  • You could add 3.
  • You could multiply by 2.
  • You could do a combination of two or more operations.
• Look at the second two terms, 6 and 9.
  • If you add 3 to 6, you get 9. So the pattern rule “add 3” seems to work.
• Make sure the pattern rule “add 3” works for every term.
  • $9+3=12$

The pattern rule works. To extend the pattern, apply the pattern rule of “add 3” to the last term, 12, to get the next term, and then “add 3” to the result to get another term. The answer is that the extended pattern is:

3, 6, 9, 12, 15, 18, . . .

You can find a particular term in the pattern by extending the pattern until you’ve reached the term you are looking for.

What is the seventh number in the following sequence?

64, 32, 16, 8, . . .

First, figure out the pattern rule. The numbers are decreasing, so the rule likely involves subtraction or division.

• Look at the first two terms, 64 and 32. What operation could you perform on 64 to get 32?
  • You could subtract 32.
  • You could divide by 2.
  • You could do a combination of two or more operations.
• Look at the second two terms, 32 and 16.
  • If you subtract 32 from 32, you get 0, not 16. So the pattern rule “subtract 32” does not work.
  • If you divide 32 by 2, you get 16. So the pattern rule “divide by 2” seems to work.
• Make sure the pattern rule “divide by 2” works for every term.
  • $16÷2=8$

The pattern rule works. To extend the pattern, apply the pattern rule of “divide by 2” to the last term, 8, to get the next term, and continue dividing by 2 until you reach the seventh term.

64, 32, 16, 8, 4, 2, 1

The seventh term of the sequence is 1.

Video: Finding Patterns in Numbers

Watch the following video to learn more identifying patterns in numbers.

Khan Academy: Finding Patterns in Numbers