Question

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?

Answer 1

• 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`

Answer 2

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)