# 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:

• 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:

• 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:

• 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:

• 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:

• 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:

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:

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:

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.