Lesson 9-3 Geometric Sequences

Presentation

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Mathematics

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9th - 12th Grade

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Practice Problem

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Easy

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CCSS.HSF.BF.A.2, geometric sequence

Standards-aligned

Steven Giesting

Used 72+ times

FREE Resource

5 Slides • 7 Questions

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, . . .

Type response here

Open Ended

Write an explicit formula for the geometric sequence

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

Type response here

Open Ended

Find the 8th term of the geometric sequence

3, 9, 27, . . .

Type response here

Open Ended

Find the 10th term of the geometric sequence

-3, 6, -12, . . .

Type response here

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, . . .

Type response here

Open Ended

Find the missing terms of the geometric sequence

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

Type response here

Lesson 9-3 Geometric Sequences

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

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