4/26 Alg1: Intro to Geometric Seqences

Introduction to Geometric Sequences

We love patterns!!!

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can identify a geometric sequence.

I can write the recursive formula for a geometric sequence.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

This represents a arithmetic sequence

This sequence starts at a value of 2, and grows by adding 3 to each term.

Relate this to linear growth.

How do you think geometric sequences will grow?

Is this sequence geometric?

Is there a common ratio? Or a common difference?

Multiple Choice

Is the sequence geometric or arithmetic?

• Geometric, there is a common ratio.

• Arithmetic, there is a common difference.

Multiple Choice

 Is the sequence geometric or arithmetic?

 $2,\ 4,\ 6,\ 8,\ 10,\ ...$  

• Geometric, there is a common ratio.

• Arithmetic, there is a common difference.

Multiple Choice

 Is the sequence geometric or arithmetic?

 $2,\ 4,\ 8,\ 16,\ 32,\ ...$  

• Geometric, there is a common ratio.

• Arithmetic, there is a common difference.

Multiple Choice

 Is the sequence geometric or arithmetic?

 $\frac{4}{3},\ \ 1\ ,\ \frac{3}{4}\ ,\frac{9}{\ 16},...$  

• Geometric

• Arithmetic

Multiple Choice

 Is the sequence geometric or arithmetic?

 $1,\ 75,\ 149,\ 223,\ 297,\ ...$  

• Geometric

• Arithmetic

Remember the equation we wrote to represent this?

There are two other ways to define sequences:

Recursive Definition

Explicit Definition

Recall the recursive definition of an arithmetic sequence.

Multiple Choice

Write the recursive formula for the geometric sequence

𝟥,𝟢𝟩𝟤, 𝟩𝟨𝟪, 𝟣𝟫𝟤, 𝟦𝟪, 𝟣𝟤,…

(Hint: What is the common ratio?)

• $a_n=2,304\left(a_{\left(n-1\right)}\right)$

• $a_n=\frac{1}{4}\left(a_{\left(n-1\right)}\right)$

• $a_n=\frac{1}{2}\left(a_{\left(n-1\right)}\right)$

Application

Want to understand the basics of investments?

What is the common ratio?

Debrief

• A geometric sequence is a number sequence in which each term after the first term is found by multiplying the previous term by a common ratio.

• Recursive definition:  $a_n=r\left(a_{\left(n-1\right)}\right)$  

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can identify a geometric sequence.

I can write the recursive formula for a geometric sequence.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Great work today! Complete your exit ticket and have a happy Monday :)