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1 vote
A

Levi just started a running plan where he runs 8 miles the first week and then
increases the number of miles he runs by 5% each week. If he keeps up this plan for
19 weeks, how many total miles would Levi have run, to the nearest whole number?

User Kelorek
by
7.5k points

2 Answers

10 votes
  • First term=a=8mi
  • Common ratio=(100+5)% =105%=1.05
  • weeks=n=19

So

It's a GP

we need Sum


\\ \rm\Rrightarrow S_n=(a(1-r^n))/(1-r)


\\ \rm\Rrightarrow S_(19)=(8(1-1.05^(19)))/(1-1.05)


\\ \rm\Rrightarrow S_(19)=(−12.21560156300510578244137725830078125)/(-0.05)


\\ \rm\Rrightarrow S_(19)=244.312\approx 244mi

User Daniel Nugent
by
7.6k points
10 votes

Answer:

244 miles (nearest whole number)

Explanation:

This scenario can be modeled as a geometric series.

From the information given:


  • a (initial term) = 8 (miles)

  • r (common ratio) = 1.05 (as number of miles increases by 5% each week)

  • n = 19 (as the plan is for 19 weeks)

The formula for the sum of the first n terms of a geometric series is:


S_n=(a(1-r^n))/(1-r)

Therefore, the sum of the first 19 terms is:


\implies S_(19)=(8(1-1.05^(19)))/(1-1.05)


\implies S_(19)=244.3120313...

Solution

244 miles (to the nearest whole number)

User Tsubasa
by
7.7k points