Recursive and Explicit Patterns

Given the following tile pattern, how many tiles would be in the 5th shape?

• 8

• 7

• 11

• 9

Based on the given pattern, how many circles would come next?

How many blocks will be in the fourth term?

• 16

• 14

• 15

• 17

What are the next two numbers in the pattern

4, 5, 1, 4, 5, 1, 4, 5, 1, ___, ___, . . .?

• 4, 5

• 5,1

Will the 10th number in the sequence 50, 45, 40, 35, 30, . . . be even or odd?

Write the explicit formula for the sequence given by 3, 6, 12, 24, …

• ^a_n= 3(2)^n-1

• ^a_n= 3+(2)ⁿ

• ^a_n= 3(2)ⁿ

• ^a_n= 3+(2)^n-1

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1 - 1

• 14

• 13

• 17

• 16

Given the recursive formula below, which is a possible explicit formula?

• a_n = 6 + 5n

• a_n = 1 + 5n

Which recursive formula can be used to define the sequence for n>1?

These patterns have rules that tell you the beginning number of a pattern and how the pattern continues. (Ex. Start at 2 and add 3 to each term.)

• Explicit Pattern

• Shrinking Pattern

• Recursive Pattern

• Pattern