ehookfin22
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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?

Respuesta :

semsee45

Answer:

244 miles (nearest whole number)

Step-by-step explanation:

This scenario can be modeled as a geometric series.

From the information given:

  • [tex]a[/tex] (initial term) = 8 (miles)
  • [tex]r[/tex] (common ratio) = 1.05 (as number of miles increases by 5% each week)
  • [tex]n[/tex] = 19 (as the plan is for 19 weeks)

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

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Therefore, the sum of the first 19 terms is:

[tex]\implies S_{19}=\dfrac{8(1-1.05^{19})}{1-1.05}[/tex]

[tex]\implies S_{19}=244.3120313...[/tex]

Solution

244 miles (to the nearest whole number)
  • First term=a=8mi
  • Common ratio=(100+5)% =105%=1.05
  • weeks=n=19

So

It's a GP

we need Sum

[tex]\\ \rm\Rrightarrow S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

[tex]\\ \rm\Rrightarrow S_{19}=\dfrac{8(1-1.05^{19})}{1-1.05}[/tex]

[tex]\\ \rm\Rrightarrow S_{19}=\dfrac{−12.21560156300510578244137725830078125}{-0.05}[/tex]

[tex]\\ \rm\Rrightarrow S_{19}=244.312\approx 244mi[/tex]

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