Problema Solution
Brian is training for a marathon. He is going to ramp up the amount of miles he runs each week by 2 miles. The first week he runs 5 miles, the second week he runs 7, the third week 9, etc/. If he keeps this up for 20 weeks, what is the total distance he will have run? Show how you arrived at your answer.
Answer provided by our tutors
1st week: 5 mi
2nd week: 7 = 5 + 2 mi
3rd week: 9 = 5 + 2*2 mi
.....
20th week: 5 + 19*2 = 43 mi
Total distance:
5 + (5 + 1*2) + (5 + 2*2) + ... + (5 + 19*2) =
= 20*5 + 2(1 + 2 + ... + 19) =
= 100 + 2(1 + 19)*19/2 =
= 100 + 20*19 =
= 100 + 380 =
= 480 mi
The total distance that Brian will ran in the period of 20 weeks is 480 miles.