Video : https://streamable.com/ynrmd3

Instructions:

• View the video found on page 1 of this journal activity.
• Using the information provided in the video, answer the questions below.
• Show your work for all calculations.

The Students' Conjectures: Two students, Ernest and Denise, are training for a swim half-marathon in 10 weeks, and they disagree about their training schedule. If they follow Ernest's suggested training schedule, will they be ready to swim 5 km in time for the half-marathon?

1. Complete the table to summarize each student's suggested training schedule. (2 points: 1 point for each row of the chart)
2. Do the distances they swim every week make an arithmetic sequence? Why? (1 point)
3. Fill out the schedules for the first four weeks of training. (2 points: 1 point for each person)
4. Write the recursive formula for each sequence: a_n = a_{n - 1} + d. (4 points: 2 point for each formula)

Student	d	Recursive formula
Ernest
Denise

1. Find the explicit formula for each arithmetic sequence: a_n = a₁ + (n - 1) d.
2. Using the explicit formula, calculate how far the students will be swimming on week 10 using Ernest's schedule. (3 points)
3. Using the explicit formula, calculate how far the students will be swimming on week 10 using Denise's schedule. (3 points)
4. Which training schedule will get them ready to swim 5 km in time for the half-marathon? (1 point)