Patterns Arithmetic and Geometric

What is the common difference of the sequence below?

• 3

• 6

• 9

• 12

What is the tenth term in the arithmetic sequence: 12, 19, 26, 33, ... Hint: Find the common difference and then either continue the pattern or write and use an explicit formula.

• 47

• 61

• 75

• 96

• 530

• 685

• 755

• 820

Write an explicit formula for the sequence 45, 40, 35, 30, ...

Write an explicit formula for the sequence 1.5, 2.0, 2.5, 3.0, ...

Write an explicit formula for the sequence -9, -7, -5, -3, ...

Now we will look at our OTHER type of sequence... We know arithmetic sequences have an adding pattern... Well GEOMETRIC sequences have a MULTIPLYING pattern. Given the sequence 3, 6, 12, 24, ..., what is the common ratio? Hint: A common ratio is the sequence's multiplier.

• 2

• 4

• 6

• 8

Arithmetic sequences form a linear equation. Geometric sequences form an exponential equation. Given the geometric sequence 2, 6, 18, ..., write an explicit formula.