Lesson 9-3 Geometric Sequences

Lesson 9-3 Geometric Sequences

Students will be able to define, identify and apply geometric sequences

Multiple Select

Identify all sequences below that are geometric

• 3, 6, 12, 24, 48, . . .

• 1, 2, 3, 4, . . .

• 1, -2, 4, -8, . . .

• 18, -6, 2,-2/3, . . .

• $1,\ \frac{1}{2},\frac{1}{3},\frac{1}{4},\ .\ .\ .$

Open Ended

Write an explicit formula for the geometric sequence

1, 2, 4, 8, . . .

Open Ended

Write an explicit formula for the geometric sequence

 $25,\ 5,\ 1,\ \frac{1}{5},\ .\ .\ .\$  

Open Ended

Find the 8th term of the geometric sequence

3, 9, 27, . . .

Open Ended

Find the 10th term of the geometric sequence

-3, 6, -12, . . .

Geometric Mean

• Take a look at this geometric sequence: -5, 15, -45, 135, -405

• Like an arithmetic sequence, the middle term of 3 consecutive terms is related

• The square of the middle term of any 3 consecutive terms is equal to the product of the other 2 terms.

• This gives us a formula for the geometric mean

• The geometric mean of two positive numbers x and y is

   $\sqrt{xy}$  

Example 1: Find the missing term

Find the missing term of the geometric sequence: 3, ___, 0.75, . . .

The missing term is the geometric mean

 $\sqrt{3\left(0.75\right)}$  

 $\sqrt{2.25}$ 

  $1.5$  

Open Ended

Find the missing term of the geometric sequence

3, ___, 12, . . .

Open Ended

Find the missing terms of the geometric sequence

-20, ___, ___, ___, -1.25, . . .