Geometric Sequences

REVIEW: LT #14 to #17

GOAL: To solidify our understanding of exponential and logarithmic equations as they apply to work, including geometric sequences.

Multiple Choice

Expand: $$\log_6\left(\frac{5}{4y}\right)$$  

• $$\log_65\ +\ \log_64\ +\ \log_6y$$  

• $$\log_65\ -\ \log_64\ +\ \log_6y$$  

• $$\log_65\ -\ \log_64\ -\ \log_6y$$  

• $$\log_65\ -\ \log_64y$$  

Multiple Choice

Expand: $$\log_4\left(3x^2\right)$$  

• $$2\log_43x$$  

• $$2\log_43\ +\ 2\log_4x$$  

• $$\log_43\ +\ 2\log_4x$$  
  

• $$2\log_43\ +\ \log_4x$$  

Multiple Choice

True or False:

log 12 - log 4 = log 8

• True

• False

Multiple Choice

Solve $$\log_2\left(x+8\right)=\log_264$$  

• x=16

• x=24

• x=56

• x=40

Multiple Choice

Solve $$\log_8\left(3x+7\right)=\log_8\left(7x+4\right)$$  

• $$x=\frac{3}{4}$$  

• $$x=3$$  

• $$x=6$$  

• $$x=\frac{4}{3}$$  

Multiple Choice

Solve $$\log_6x+\log_69=\log_654$$  

• x=6

• x=45

• x=7

• x=36

Multiple Choice

log₂(x + 2) + log₂x  = 3

• -4, 2
• -2, 4
• 2
• 1

Multiple Choice

Solve

• A
• B
• C
• D

Multiple Choice

• 5
• 13
• 84
• -20

Multiple Choice

Solve for x:

$$12\cdot\ 2^{\left(x-7\right)}=24$$

• $$x=8$$

• $$x=-6$$

• $$x=19$$

• $$x=\frac{1}{7}$$

Multiple Choice

Using a calculator approximate ln 2.3 to the nearest thousandth

• .8322

• .8329

• .8320

• .9238

Multiple Choice

Rewrite in exponential form:
ln(2) = x

• 2^x = 10
• 10² = x
• e^x = 2
• e² = x

Multiple Choice

Which of the following is the value of x given;
7e^(3x-5) = 49

• x = 2.315
• x = 0.681
• x = 2.964
• No Solution

Multiple Choice

What do you notice about the following sequence;

40, 120, 360, 1080, 3240, ...

• Each term gets multiplied by 3; starting with 40.

• Each term increases by 80

• Each term is raised to the third power.

• There is no relationship between the values.

Multiple Choice

What do you notice about the following sequence;

256, 192, 144, 108, 81, ...

• Each term is multiplied by 0.75

• Each term is divided by 0.75

• Each term is doubled

• There is no relationship between the terms.

Multiple Choice

So - considering all of that. Given the sequence;

3, 6, 12, 24, ...

Find the next two terms

• 36, 48,...

• 48, 96,...

• 27, 30,...

• None of these are the correct next terms.

Multiple Choice

Find the common ratio for the geometric sequence.

• 10
• 1/2
• 2
• 4

Multiple Choice

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Multiple Choice

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

• 20, 100, 500, 2500
• 5, 20, 80, 320
• 4, 20, 100, 500
• 4, 9, 14, 19

Multiple Choice

If we say a value DECREASES at a rate of 22%, what is the multiplier (r) we would use? Fee free to pick a value and find the first few terms.

• 22

• 0.22

• 78

• 0.78

Multiple Choice

A sequence starts at 100 and decreases by 43%. What is the multiplier (r) we would use? Again, if needed pick a value and find the first couple of terms to evaluate.

• 0.43

• 0.57

• 43

• 57

Multiple Choice

A sequence starts at 100 and decreases by 43%. Find the EXPLICIT formula for this sequence.

• a_n = 100 * 0.57^n-1

• a_n = 100 * 0.43^n-1

• a_n = 100 * 1.57^n-1

• a_n = 100 * 1.43^n-1

Multiple Choice

A sequence starts at 100 and decreases by 43%. Find the value of the 10th term. (n = 10)

• a₁₀ = 0.6351

• a₁₀ = 0.0216

• a₁₀ = 0.3620

• a₁₀ = 9099.060

Open Ended

Will a geometric sequence ever lead to an output of zero? Why or why not?