Question

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.

Answer 1

110 miles

Explanation:

First week = 2 miles

Additional miles per week = 2 miles

This sum of miles ran in the first 10 week canbe obtained using the relation :

: n/2[2a + (n-1)d]

n = 10

d = common difference = additional miles ran = 2

a = first term = first week miles = 2

10/2[2(2) + (10-1)2]

5[4 + 9*2]

5[4 + 18]

5[22]

= 110 miles

Miles