- Description
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.