Question

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

244 miles (nearest whole number)

Explanation:

We can model this as a geometric series.

General form of a geometric sequence:
`a_n=ar^(n-1)`

(where a is the first term and r is the common difference)

Given information:

• Miles run in first week = 8
• Weekly increase of miles = 5%
• Total number of weeks in plan = 19

Therefore:

• 
  `a` = 8
• 
  `r` = 1.05
• 
  `n` = 19

Sum of the first n terms of a geometric series:

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

Therefore, sum of the first 19 terms:

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

`\implies S_(19)=244.3120313...`

So Levi ran a total of 244 miles (to the nearest whole number)