A2 Final Exam Review 22-23 S1 (Pt. 2)

Algebra 2 CP Final Exam Review Pt. 2

Topic: Arithmetic and Geometric Sequences

This assignment counts as a minor grade. Please complete it twice if your first grade is unsatisfactory.

Arithmetic Sequence

An arithmetic sequence is a sequence where you add a constant number to find the next term, similar to the constant rate of change in a linear function.

In an arithmetic sequence we only add to find the next number (term). This number can be positive or negative.

Term

In a sequence each number is called a term.

The dots at the end mean the sequence continues forever.

a₁ is the first term

a₂ is the second term

a₃ is the third term and so on...

a_n is the nth term (we will find the equation for the nth term in the next lesson)

Ready to try some examples?

Remember in an arithmetic sequence, each number is found by adding a common difference, which can be positive or negative.

Multiple Choice

What is each number in a sequence called?

• common difference

• term

• sequence

• arithmetic

Multiple Choice

What is the difference between two numbers in an arithmetic sequence called?

• common difference

• term

• sequence

• number

Multiple Choice

Identify the common difference.

10, 20, 30, 40, ...

• 5

• 10

• 15

• 20

Multiple Choice

Find the common difference: 29, 21, 13, 5, ...

Remember, the common difference is the difference between the numbers.

• d = -10

• d = -9

• d = -8

• d = -7

Multiple Select

Which sequences are arithmetic?

(hint: select 2)

• 2, 4, 6, 8, 10 ...

• 5, 10, 20, 40, 80, 100 ...

• 1, 3, 7, 9, 15, 20 ...

• 4, 8, 12, 16, 20, 24 ...

Multiple Choice

If the first term of an arithmetic sequence is 5 and the common difference is 6, what are the first five terms?

• 5, 11, 17, 23, 29

• 6, 11, 16, 21, 26

• 5, 10, 15, 20, 25

• 5, 11, 15, 20, 26

Multiple Choice

Which sequence has a common difference of 4?

• 4, 6, 8, 10, 12...

• 1, 5, 9, 13, 17....

• 4, 4, 4, 4, 4...

• 4, 14, 24, 34, 44...

Multiple Choice

Is the sequence Arithmetic?

10, 18, 26, 34, 40

• Yes

• No

Multiple Choice

Is this an arithmetic sequence?

1, 5, 9, 13, ...

• yes

• no

Open Ended

What is the common difference of this arithmetic sequence:

1, 5, 9, 13, ...

Multiple Choice

Is this an arithmetic sequence?

1, 3, 6, 10, ...

• yes

• no

Multiple Choice

Is this an arithmetic sequence?

6, 2, -2, -6, ...

• yes

• no

Open Ended

What is the common difference of this arithmetic sequence:

6, 2, -2, -6, ...

Open Ended

What are the next 2 terms of this arithmetic sequence:

12, 9, 6, 3, ...

Open Ended

What are the next 2 terms of this arithmetic sequence:

-2, 2, 6, 10, ...

Sequences

A sequence is an ordered list of numbers. Each number in a sequence is called a term. Each term an has a specific position n in the sequence.

example: 5, 10, 15, 20, 25,…a_n

Multiple Choice

 The formula for finding the $$n^{th}$$  term of the arithmetic sequence:

15, 13, 11, 9 ... * what is the first term? * what is the common difference?

• $$15+\left(n-1\right)\left(2\right)$$  

• $$9+\left(n-1\right)\left(2\right)$$  

• $$15+\left(n-1\right)\left(-2\right)$$  

Fill in the Blank

Find 141st term of the arithmetic sequence: 15, 13, 11, 9... 1) Use the formula  $$a_n=a_1+\left(n-1\right)\left(d\right)$$ 2. Replace $$n$$  with the term you are looking for ( $$141$$   )

3. Replace $$a_1$$  with the first tern in the arithmetic sequence ( $$15$$  ) 

4. Say to yourself, this is why I was told to have a calculator ;) 5. The 141st term of the arithmetic sequence is _______

we also have special sequence formulas to learn

Multiple Choice

Find the 10^th term in the sequence that starts with 1 and has a common difference of 3.

• 28

• 25

• 24

• 26

Fill in the Blank

If the sequence 6, 11, 16, 21 continues, what will be the 9^th term?

Geometric Sequences

Is multiplied or divided by the same value every time

Multiple Choice

What does r represent?

• Radical

• Common difference

• Common ratio

Multiple Choice

Find the common ratio for the geometric sequence.

• 10

• 1/2

• 2

• 4

Multiple Choice

Find the common ratio of the following geometric sequence:

2, -10, 50, -250, ...

• r = -5

• r = 3

• r = 5

• r = -3

Multiple Choice

Is this sequence geometric?

• yes

• no

Multiple Choice

Is the sequence 2, 4, 12, 48,... geometric?

• yes

• no

Multiple Choice

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

• 324, 972, 2916

• 972, 2916, 8748

• 405, 1215, 3645

Two different ways to show the same thing

Some text here about the topic of discussion

​Explicit Formua

​Recursive Formula

Multiple Choice

What would term a₁ be in the sequence:

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

• 16

• 8

• 4

• 32

Multiple Choice

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

If a₄ = 40, what would a_n-1 be?

• 5

• 10

• 20

• 40

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 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​

​

​

​Some text here about the topic of discussion.

​Explicit Formula

​

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

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

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 4

• 3

• 2

• 6

Multiple Choice

A plumber charges $55 for 1 hour of work, $90 for 2 hours, and $125 for 3 hours. Which function represents the sequence of hourly charges?

• $$a_n=35(55)^{n-1}$$

• $$a_n=55(35)^{n-1}$$

• $$a_n=35+55(n-1)$$

• $$a_n=55+35(n-1)$$

Multiple Choice

Select the explicit rule that represents the sequence.

• A=1+5n

• A=6+5n

• A = 5+1n

• A=5+6n

Multiple Choice

Select the explicit rule that represents the sequence.

• A=14-3n

• A=3-14n

• A=17-3n

• A=3-17n