Introduction to Algebraic and Geometric Sequences

​M3 L3 Arithmetic & Geometric SEQUENCES

Multiple Choice

How would you describe the overall pattern for this sequence of number?

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

• It’s an adding/subtracting pattern

• It’s a multiplying/dividing pattern

Multiple Choice

What is the exact “common pattern“ for this particular sequence?

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

• Add -5

  (Which means subtract 5)

• Add 5

• Multiply by 5

• Multiply by -5

Multiple Choice

Is the sequence below arithmetic or geometric?

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

• Arithmetic because the pattern is adding

• Geometric because the pattern is multiplying

Multiple Choice

CHALLENGE: This sequence is geometric, so it represents an exponential pattern. Which picture better represents the graph of this exponential function?

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Multiple Choice

An exponential function represents a  ________ sequence.

Hint: Multiply/Divide by a common ratio (r)

• Arithmetic

• Geometric

Multiple Choice

An linear function represents a  ________ sequence.

Hint: add/subtract by a common difference (d)

• Arithmetic

• Geometric

Multiple Choice

Given the sequence

3, 6, 9, 12, …

What is $$a_1$$  

• 1

• 3

Multiple Choice

$$If\ a_6=100$$  

$$n=6$$  

True or False?

• TRUE

  $$a_{6\ }$$  means the 6th term so n=6

• FALSE

  $$a_6=100$$  Means the 100th term so n=100

Multiple Choice

$$a_3=21$$  

Which statement best describes the sequence notation?

• The third term of the sequence is 21

• The 21st term of the sequence is 3

• The first term of the sequence is 3

• This is a geometric sequence.

Multiple Select

Which formulas are recursive:

Hint: there are two answers

• $$a_n=a_{\left(n-1\right)}+10$$  

• $$a_n=5\cdot a^{\left(n-1\right)}$$  

• $$a_n=5n-1$$  

Take detailed notes as we evaluate this sequence together.

Given the following sequence:

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

​

• ​

​

​

• Find the common pattern

• ​Write the nth term recursive formula

• ​Write the nth term explicit formula

• Find the 99th term.

Multiple Select

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

Is this sequence arithmetic or geometric?

• Arithmetic

• Geometric

Fill in the Blank

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

What is the common difference between each term?

Enter your number answer only.

Multiple Select

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

What will a picture of the graph look like if it is an arithmetic sequence?

• A line that has steady growth

• An exponential graph that “takes off like a rocket” and grows really fast

Multiple Choice

Choose the recursive formulas that correctly represent this sequence:

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

• $$a_n=a_{n-1}+4$$

• $$a_n=4\left(n-1\right)-2$$

• $$a_n=a_{n-1}\cdot4$$

Multiple Select

Choose all the explicit formulas matches this sequence?

Hint: there are two answers

-2, 2, 6, 10,... 

• $$a_n=6n-4$$  

• $$a_n=4n-2$$  

• $$a_n=-2+4\left(n-1\right)$$  

• $$a_n=4n-6$$  

Fill in the Blank

 Find the 99th term for the sequence -2, 2, 6, 10, ... 

Type the number answer only

​​Do you know how to write both….

​Sequence and Function Notation for the 99th term?

I will give you 3-4 minutes to answer the following questions on your paper. When time is up, you will enter your answers in Quizizz.

Given -1, 6, -36, 216

​

• Arithmetic or Geometric?

• Write an explicit formula.

• Write a recursive formula.

• Find the 8th term.

Multiple Select

Which best describes this sequence based on the common pattern?

-1, 6, -36, 216

• Arithmetic

• Geometric

Fill in the Blank

What is the common ratio?

-1, 6, -36, 216

Enter the number answer only.

Open Ended

Challenge: Would it be possible to write an arithmetic formula for this sequence? Why or why not?

-1, 6, -36, 216

Multiple Select

Choose all that represent an explicit geometric formula

 formula?

Hint: There is more than one correct answer

-1, 6, -36, 216

• $$a_n=a_{n-1}\cdot\left(-6\right)$$

• $$a_n=a_{n-1}-6$$

Multiple Select

Choose all that represent a recursive geometric formula

 formula?

Hint: There is more than one correct answer

-1, 6, -36, 216

• $$a_n=a_{n-1}\cdot\left(-6\right)$$

• $$a_n=-6\left(a_{n-1}\right)$$

Fill in the Blank

Find the 8th term

-1, 6, -36, 216

Enter your answer with no commas or spaces…digits only

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Open Ended

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