Answer: If Amanda runs two miles the first week and then adds two miles each subsequent week, we can create a sequence using arithmetic progression. The common difference between each term in the sequence is two, and the first term is two.
Using the formula for the nth term of an arithmetic progression, we can find the number of miles Amanda would run in the first 10 weeks of her training:
an = a1 + (n-1)d
where:
an = the nth term of the sequence
a1 = the first term of the sequence (2 miles in the first week)
n = the number of terms (up to 10 weeks)
d = the common difference between each term (2 miles per week)
So for n = 1 to 10, we have:
a1 = 2
d = 2
n = 1: a1 + (n-1)d = 2 + (1-1)2 = 2
n = 2: a1 + (n-1)d = 2 + (2-1)2 = 4
n = 3: a1 + (n-1)d = 2 + (3-1)2 = 6
n = 4: a1 + (n-1)d = 2 + (4-1)2 = 8
n = 5: a1 + (n-1)d = 2 + (5-1)2 = 10
n = 6: a1 + (n-1)d = 2 + (6-1)2 = 12
n = 7: a1 + (n-1)d = 2 + (7-1)2 = 14
n = 8: a1 + (n-1)d = 2 + (8-1)2 = 16
n = 9: a1 + (n-1)d = 2 + (9-1)2 = 18
n = 10: a1 + (n-1)d = 2 + (10-1)2 = 20
Therefore, Amanda would run 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 miles in the first 10 weeks of her training if she followed the new regimen.
Explanation: