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.