1. Amanda is training to run a marathon. She must follow a strict schedule to make sure she is ready for the race. She will start her training by running two miles the first week. She wants to run one fewer mile the next week, and then three more miles the week after that. She will continue this pattern during her entire training regimen. a. Write a sequence for the number of miles that Amanda will run the first 10 weeks of her training. Explain your reasoning.

b. In which week of training will Amanda run seven miles?

c. Amanda needs to run 26 miles in the final week of her training. In which week will Amanda reach her goal? Explain your answer.

d. Amanda is considering changing her regimen by running two miles the first week and then running an additional two miles each subsequent week. Write a sequence for the number of miles that Amanda would run the first 10 weeks of her training if she followed the new regimen. Explain your reasoning.

e. In which week would Amanda reach her goal of 26 miles, if she followed the new regimen? Explain your reasoning.

2. Amanda chooses to continue with the first training regimen. Because it will take a long time to train, Amanda decides that during her periods of rest, she will sew a quilt to have as a remembrance of her achievement. She will add squares to the quilt every two weeks using the pattern shown (added squares are shaded). Weeks 1 and 2 Weeks 3 and 4 Weeks 5 and 6

a. Write a sequence for the first 10 terms generated by this situation. Each term should represent the number of squares that the quilt will have. The first term has one square. Explain your reasoning.

b. By the end of her training regimen, how many squares will the quilt have? Explain your reasoning.