Geometric Sequence and Means

Which of the following is a geometric sequence?

• 3, 6, 9, 12, 15, …

• 2, 6, 18, 54, 162, …

• . 5, 8, 11, 14, 17, …

• 4, 8, 12 ,16, 20, …

What is the common ratio of the geometric sequence 5, 10, 20, 40?

• 2

• 5

• 10

• 20

What is the common ratio of the geometric sequence 15, 30, 60, 120?

• 2

• 3

• 15

• 20

What is the geometric mean between 8 and 288

• 48

• 58

• 68

• 78

Insert two geometric means between 9 and 1 125

• 45, 225

• 50, 250

• 55, 260

• 60, 265

Insert three geometeric means between 12 and 49 152

• 95, 767, 6 044

• 96, 768, 6 144

• 97, 769, 6 244

• None of these

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.

Given the geometric sequence 64, 16, 4, 1, ..., write an explicit formula.