**Answer** the following in 175 to 260 words in your commentary:

- How does the graph of a line compare to an arithmetic sequence? What does the slope represent? How would you find the first term?
- Use your best fit equation to make a formula for the nth term of an arithmetic sequence. The year will represent the number of the term, and your data value will be the value at that term.
- Use your arithmetic equation to predict what the 2,050th term will be. Do you think this is a good estimate of what the real value will be? Why or why not?

**Challenge Option**

**Open** your Microsoft^{®} Excel® file from Week 2 with your exponential graph.

**Click** “Save As” to create a new version of this file.

**Delete** the old commentary.

**Answer** the following by adding new commentary:

- How does the graph of an exponential equation compare to a geometric sequence? How would you find the common ratio? How would you find the first term (assuming the year is the number of the term)?
- Use your best fit equation to make a formula for the nth term of a geometric sequence. The year will represent the number of the term, and your data value will be the value at that term.
- Use your geometric equation to predict what the 2,050th term will be. Do you think this is a good estimate of what the real value will be? Why or why not?

**Save** your Microsoft^{®} Excel® file, including your old graphed equation and new commentary. Make sure you do not delete your files, as you will need them in subsequent weeks.