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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 25
^{th}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*.

- Provide an example and the steps you would take to solve for these terms.

**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*v*= (Dream car Price)(3/4)_{n},^{n}*n*= 1, 2, 3...- Find the fifth term and explain what this value represents.
- Describe the
*n*th 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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