Geometric Sequences

Presentation

•

Mathematics

•

9th - 12th Grade

•

Hard

Joseph Anderson

FREE Resource

11 Slides • 26 Questions

Geometric Sequences

Two different ways to show the same thing

Some text here about the topic of discussion

Explicit Formula

Recursive Formula

Multiple Choice

What would term a₁ be in the sequence:

4, 8, 16, 32, 64, ...

Multiple Choice

What is the common ratio (r) in the sequence:

4, 8, 16, 32, 64, ...

Multiple Choice

What is the common ratio (r) in the sequence:

-2, 16, -128, 768, -6144, ...

-8

Multiple Choice

Using the sequence: 5, 10, 20, 40, 80, 160, ...

If a₄= 40, what would a_n-1 be?

Find a₁ ---> the first term

Understand what a_n-1 means.... it means the previous term

Recursive Formula

Multiple Choice

Given the sequence: 3, 12, 48, 96, 384, ...

What is a₁?

Multiple Choice

Given the sequence: 3, 12, 48, 96, 384, ...

What is r?

Multiple Choice

Given the sequence: 3, 12, 48, 96, 384, ...

What is the recursive formula?

a₁= 3

a_n= (4) a_n-1

a₁= 4

a_n= (3) a_n-1

a₁= 12

a_n= (9) a_n-1

a₁= 3

a_n= (-9) a_n-1

a₁= first term

r = common ratio

n - 1 = previous term

n = desired term

Explicit Formula

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

What is a₁?

3750

150

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

What is r?

3750

150

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

What is the explicit formula?

a_n= 5*(5)^n-1

a_n= 30*(6)^n-1

a_n= 6*(30)^n-1

a_n= 6*(15)^n-1

Multiple Choice

Given the sequence: 6, 30, 150, 750, 3750, ...

Use the explicit formula from the previous slide to the find the 8th term?

3750

475068

468750

Example: 120, 60, 30, 15, 7.5, ...

Sequences can also decrease as well. If the common ratio is less than 1, the sequence decays or declines

Common ratio less than 1

64, 32, 16, 8, 4, ...

r = 1/2

Decay

Common ratio greater than 1

4, 8, 16, 32, 64, ...

r = 2

Growth

The common ratio determines if the sequence is growth vs. decay

Multiple Choice

Is the following sequence a growth or decay?

7, 49, 343, 2401, 16807, ...

Growth

Decay

Multiple Choice

Is the following sequence a growth or decay?

-20, -60, -360, -2160, -12,960, ...

Growth

Decay

Multiple Choice

Find the next three terms: 4, 12, 36, 108, ...

324, 972, 2916

972, 2916, 8748

405, 1215, 3645

Multiple Choice

What is the recursive rule for the sequence:
11, 22, 44, 88...

a_n = 2(11)^n-1

a_n = 11x 2

a_n = 11(2)^n-1

a_n = 2a_n-1

Multiple Choice

Given the sequence:
125, 25, 5, ....
Write the explicit rule:

t(n) = (125)(5)⁽ⁿ⁾

t(n) = 625(1/5)⁽ⁿ⁾

t(n) = 625(5)⁽ⁿ⁾

t(n) = 125 + 5n

Multiple Choice

Find the general rule for: 64, -32, 16, -8, …

64(1/2)^n-1

(-32)^n-1

64(-1/2)^n-1

(32)^n-1

Multiple Choice

Which sequence is represented by the equation 2(7)^n-1 ?

7, 14, 28, 56...

2, 14, 98, 686...

2, 9, 16, 23...

7,9,11,13...

GEOMETRIC SERIES

The sum of the terms in a geometric sequence.

GEOMETRIC SERIES

Multiple Choice

What is the formula to be used in finding the sum of the first five terms of the sequence 5,15,45,...?

$S_n=\frac{n}{2}\left(a_1+a_n\right)$

$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$

Fill in the Blanks

Type answer...

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INFINITE GEOMETRIC SERIES

Multiple Choice

Find the indicated sum of the geometric sequence if its first term is 318 and the common ratio is one-half. Is the problem an example of INFINITE GEOMETRIC SERIES?

Yes, it is!

No, it is not!

Multiple Choice

What is the formula to be used to solve the problem?

$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$

$S_{\infty}=\frac{a_1}{1-r}$

Fill in the Blanks

Type answer...

Geometric Sequences

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