Lesson 3 12 Concept Geometric Sequences EQ How
![Lesson 3. 12 Concept: Geometric Sequences EQ: How do we recognize and represent geometric Lesson 3. 12 Concept: Geometric Sequences EQ: How do we recognize and represent geometric](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-1.jpg)
![Activator: First Word Using the word ‘EXPONENTIAL’, create a phrase starting with each letter Activator: First Word Using the word ‘EXPONENTIAL’, create a phrase starting with each letter](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-2.jpg)
![Introduction • A geometric sequence is a list of terms separated by a common Introduction • A geometric sequence is a list of terms separated by a common](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-3.jpg)
![Introduction (continued) Just like arithmetic sequences, Geometric sequences can be represented by formulas, either Introduction (continued) Just like arithmetic sequences, Geometric sequences can be represented by formulas, either](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-4.jpg)
![First Term Current Term Common Ratio Previous Term 5 3. 11: Geometric Sequences First Term Current Term Common Ratio Previous Term 5 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-5.jpg)
![Steps to create formulas and solve for geometric sequences 1. Find the common ratio Steps to create formulas and solve for geometric sequences 1. Find the common ratio](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-6.jpg)
![Guided Practice Example 1 Create the recursive formula that defines the sequence: A geometric Guided Practice Example 1 Create the recursive formula that defines the sequence: A geometric](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-7.jpg)
![Guided Practice Example 1, continued Create the recursive formula that defines the sequence: A Guided Practice Example 1, continued Create the recursive formula that defines the sequence: A](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-8.jpg)
![9 3. 11: Geometric Sequences 9 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-9.jpg)
![Step 1: Find the common ratio Step 3: Substitute what you have Step Step 1: Find the common ratio Step 3: Substitute what you have Step](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-10.jpg)
![Step 1: Find the common ratio Step 3: Substitute what you have Step Step 1: Find the common ratio Step 3: Substitute what you have Step](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-11.jpg)
![12 3. 11: Geometric Sequences 12 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-12.jpg)
![13 3. 11: Geometric Sequences 13 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-13.jpg)
![14 3. 11: Geometric Sequences 14 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-14.jpg)
![Guided Practice Example 5 Write an explicit formula to represent the sequence from example Guided Practice Example 5 Write an explicit formula to represent the sequence from example](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-15.jpg)
![Guided Practice: Example 5, continued The first five terms of the sequence are: 2, Guided Practice: Example 5, continued The first five terms of the sequence are: 2,](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-16.jpg)
![Guided Practice Example 6 Write an explicit formula to represent the sequence from example Guided Practice Example 6 Write an explicit formula to represent the sequence from example](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-17.jpg)
![Guided Practice: Example 6, continued The first five terms of the sequence are: 6, Guided Practice: Example 6, continued The first five terms of the sequence are: 6,](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-18.jpg)
![Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? Step Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? Step](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-19.jpg)
![Summary: Last word Using the word ‘GEOMETRIC’, create a phrase with each letter just Summary: Last word Using the word ‘GEOMETRIC’, create a phrase with each letter just](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-20.jpg)
- Slides: 20
![Lesson 3 12 Concept Geometric Sequences EQ How do we recognize and represent geometric Lesson 3. 12 Concept: Geometric Sequences EQ: How do we recognize and represent geometric](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-1.jpg)
Lesson 3. 12 Concept: Geometric Sequences EQ: How do we recognize and represent geometric sequences? F. BF. 1 -2 & F. LE. 2 Vocabulary: Geometric Sequence, Common ratio, Explicit formula, Recursive formula 1 3. 11: Geometric Sequences
![Activator First Word Using the word EXPONENTIAL create a phrase starting with each letter Activator: First Word Using the word ‘EXPONENTIAL’, create a phrase starting with each letter](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-2.jpg)
Activator: First Word Using the word ‘EXPONENTIAL’, create a phrase starting with each letter in the word on a sheet of paper. To get you started, I will give you an example. Exponential graphs looks like a ‘J’ curve. X P O N E N T I A L Now you finish the rest. 2 3. 8. 2: Geometric Sequences
![Introduction A geometric sequence is a list of terms separated by a common Introduction • A geometric sequence is a list of terms separated by a common](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-3.jpg)
Introduction • A geometric sequence is a list of terms separated by a common ratio, r, which is the number multiplied by each consecutive term in a geometric sequence. • A geometric sequence is an exponential function with a domain of whole numbers in which the ratio between any two consecutive terms is equal. 3 3. 11: Geometric Sequences
![Introduction continued Just like arithmetic sequences Geometric sequences can be represented by formulas either Introduction (continued) Just like arithmetic sequences, Geometric sequences can be represented by formulas, either](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-4.jpg)
Introduction (continued) Just like arithmetic sequences, Geometric sequences can be represented by formulas, either explicit or recursive, and those formulas can be used to find a certain term of the sequence or the number of a certain value in the sequence. Recall • A recursive formula is a formula used to find the next term of a sequence when the previous term is known. • An explicit formula is a formula used to find the nth term of a sequence. 4 3. 11: Geometric Sequences
![First Term Current Term Common Ratio Previous Term 5 3 11 Geometric Sequences First Term Current Term Common Ratio Previous Term 5 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-5.jpg)
First Term Current Term Common Ratio Previous Term 5 3. 11: Geometric Sequences
![Steps to create formulas and solve for geometric sequences 1 Find the common ratio Steps to create formulas and solve for geometric sequences 1. Find the common ratio](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-6.jpg)
Steps to create formulas and solve for geometric sequences 1. Find the common ratio by dividing the 2 nd term by the 1 st term. 2. Decide which formula to use. (explicit or recursive) 3. Substitute your values to create your formula. 4. Find the specific term if asked to do so. 3. 8. 2: Geometric Sequences 6
![Guided Practice Example 1 Create the recursive formula that defines the sequence A geometric Guided Practice Example 1 Create the recursive formula that defines the sequence: A geometric](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-7.jpg)
Guided Practice Example 1 Create the recursive formula that defines the sequence: A geometric sequence is defined by 2, 8, 32, 128, … 7 3. 11: Geometric Sequences
![Guided Practice Example 1 continued Create the recursive formula that defines the sequence A Guided Practice Example 1, continued Create the recursive formula that defines the sequence: A](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-8.jpg)
Guided Practice Example 1, continued Create the recursive formula that defines the sequence: A geometric sequence is defined by 2, 8, 32, 128, … 8 3. 11: Geometric Sequences
![9 3 11 Geometric Sequences 9 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-9.jpg)
9 3. 11: Geometric Sequences
![Step 1 Find the common ratio Step 3 Substitute what you have Step Step 1: Find the common ratio Step 3: Substitute what you have Step](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-10.jpg)
Step 1: Find the common ratio Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? 10 3. 11: Geometric Sequences
![Step 1 Find the common ratio Step 3 Substitute what you have Step Step 1: Find the common ratio Step 3: Substitute what you have Step](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-11.jpg)
Step 1: Find the common ratio Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? 11 3. 11: Geometric Sequences
![12 3 11 Geometric Sequences 12 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-12.jpg)
12 3. 11: Geometric Sequences
![13 3 11 Geometric Sequences 13 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-13.jpg)
13 3. 11: Geometric Sequences
![14 3 11 Geometric Sequences 14 3. 11: Geometric Sequences](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-14.jpg)
14 3. 11: Geometric Sequences
![Guided Practice Example 5 Write an explicit formula to represent the sequence from example Guided Practice Example 5 Write an explicit formula to represent the sequence from example](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-15.jpg)
Guided Practice Example 5 Write an explicit formula to represent the sequence from example 1, and find the 10 th term. The first five terms of the sequence are: 2, 8, 32, 128, and 512. 15 3. 11: Geometric Sequences
![Guided Practice Example 5 continued The first five terms of the sequence are 2 Guided Practice: Example 5, continued The first five terms of the sequence are: 2,](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-16.jpg)
Guided Practice: Example 5, continued The first five terms of the sequence are: 2, 8, 32, 128, and 512. 16 3. 11: Geometric Sequences
![Guided Practice Example 6 Write an explicit formula to represent the sequence from example Guided Practice Example 6 Write an explicit formula to represent the sequence from example](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-17.jpg)
Guided Practice Example 6 Write an explicit formula to represent the sequence from example 3, and find the 15 th term. The first five terms of the sequence are: 6, -18, 54, -162, and 486 17 3. 11: Geometric Sequences
![Guided Practice Example 6 continued The first five terms of the sequence are 6 Guided Practice: Example 6, continued The first five terms of the sequence are: 6,](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-18.jpg)
Guided Practice: Example 6, continued The first five terms of the sequence are: 6, -18, 54, -162, and 486 Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? Step 4: Evaluate for specific term 18 3. 11: Geometric Sequences
![Step 3 Substitute what you have Step 2 Explicit or Recursive Formula Step Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? Step](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-19.jpg)
Step 3: Substitute what you have Step 2: Explicit or Recursive Formula? Step 4: Evaluate for specific term 19 3. 11: Geometric Sequences
![Summary Last word Using the word GEOMETRIC create a phrase with each letter just Summary: Last word Using the word ‘GEOMETRIC’, create a phrase with each letter just](https://slidetodoc.com/presentation_image_h/a92f7d83e22c39479457ebb539ce9e37/image-20.jpg)
Summary: Last word Using the word ‘GEOMETRIC’, create a phrase with each letter just like with exponential from before. 20 3. 8. 2: Geometric Sequences
Lesson 3: arithmetic and geometric sequences
Section 7 topic 1 geometric sequences answers
10-3 geometric sequences and series
Formulas
10-3 geometric sequences and series answer key
Recursive sequence formula
Exponential number sequence
What is a explicit formula
Geometric formula
Arithmetic series formula
Recursive formula for geometric sequence
Geometric formula
9-1 geometric sequences
Sum of gp formula
Geometric sequences gcse
Sequences notes
Geometric sequences formula
Arithmetic sequence
Geometric sequences
Arithmetic and geometric patterns
Geometric sequence