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MTH 220 Week 4 Participation Prompt Week 4, Day 5 (Saturday)

MTH 220 Week 4 Participation Prompt Week 4, Day 5 (Saturday)

In this learning activity, discuss with the other members of your group your experiences with arithmetic and geometric sequences and series.

Post a 150-word response to one of the discussion prompts by Day 5 in the discussion area below:

Prompt 1

View one of the following Week 4 videos:

 

 

 

Khan Academy: Sequences Intro
 

 

Khan Academy: Evaluating Sequences in Recursive Form
 

 

Patrick Just Math Tutorials: Arithmetic Sequences: A Quick Intro
 

 

Khan Academy: Intro to Arithmetic Sequences
 

 

Khan Academy: Explicit Formulas for Arithmetic Sequences
 

 

 

Answer the following question:

 

 

 

Given any sequence, how can you determine if it is an arithmetic sequence? Provide an example in your explanation.
 

 

 

Prompt 2

View one of the following Week 4 videos:

 

 

 

Khan Academy: Evaluating Sequences in Recursive Form
 

 

Patrick Just Math Tutorials: Arithmetic Sequences: Finding a General Formula Given Two Terms
 

 

Khan Academy: Sequences Intro
 

 

 

Answer the following questions:

 

 

 

If you were given a recursion formula, how would you determine the next three terms? How would you determine the 25th term? 

 

 

 

Provide an example and the steps you would take to solve for these terms. Hint: Use a recursion formula found on p. 708 of College Algebra.
 

 

 

 
 

 

 

Prompt 3

View one of the following Week 4 videos:

 

 

 

Khan Academy: Intro to Finite Arithmetic Series
 

 

Khan Academy: Sigma Notation for Sums
 

 

 

Answer the following question:

 

 

 

Suppose you are provided with an arithmetic sequence. How can you find the sum of n terms of the sequence without having to add all of the terms? Provide an example in your explanation.
 

 

 

Prompt 4

View the following Week 4 videos:

 

 

 

Patrick Just Math Tutorials: Geometric Sequences: A Quick Intro
 

 

Patrick Just Math Tutorials: Arithmetic Sequences: A Quick Intro
 

 

 

Answer the following question:

 

 

 

With any sequence, how can you determine which type of sequence it is? Provide an example in your explanation.
 

 

 

Prompt 5

View one of the following Week 4 videos:

 

 

 

Khan Academy’s: Finite Geometric Series
 

 

Khan Academy’s: Finite Geometric Series Word Problem: Social Media
 

 

 

Answer the following question:

 

 

 

Suppose you are provided with a geometric sequence. How can you find the sum of n terms of the sequence without having to add all of the terms? Provide an example in your explanation.
 

 

 

Prompt 6

View one of the following Week 4 videos:

 

 

 

Patrick Just Math Tutorials: Geometric Sequences: A Quick Intro
 

 

Khan Academy: Using Explicit Formulas of Geometric Sequences
 

 

Khan Academy: Finite Geometric Series
 

 

Khan Academy: Finite Geometric Series Word Problem: Social Media
 

 

 

Solve the following problem:

 

 

 

Research the price of the car of your dreams. Calculate the value it would be at the end of n years with the sequence vn = (Dream car Price)(3/4)n, n = 1, 2, 3… 

 

 

 

Find the fifth term and explain what this value represents.
 

 

Describe the nth term of the sequence in terms of the value of your car at the end of each year.
 

 

 

 
 

 

 

Prompt 7

View one of the following Week 4 videos:

 

 

 

Patrick Just Math Tutorials: Geometric Sequences: A Quick Intro
 

 

Khan Academy: Explicit and Recursive Formulas of Geometric Sequences
 

 

Khan Academy: Using Explicit Formulas of Geometric Sequences
 

 

 

Solve the following problem:

 

 

 

A ball is bouncing to a height that is one third of the previous height after every bounce. 

 

 

 

What kind of sequence is this?
 

 

How could you find the total distance travelled by the ball? Provide an example in your explanation.
 

 

 

 
 

 

 

Prompt 8

View one of the following Week 4 videos:

 

 

 

Khan Academy: Sequences Intro
 

 

Patrick Just Math Tutorials: Geometric Sequences: A Quick Intro
 

 

 

Solve the following problem:

 

 

 

One person tells another individual a rumor and that individual tells two people, then they both tell two other people. 

 

 

 

Is this considered an arithmetic or geometric sequence? Explain your answer.
 

 

 

 
 

 

 

Note: All Khan Academy content is available for free at www.khanacademy.org.

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