Question

Parker just started a running plan where he runs 7 miles the first week and then

increases the number of miles he runs by 10% each week. If he keeps up this plan for
15 weeks, how many total miles would Parker have run, to the nearest whole
number?

Answer 1

To find the total number of miles Parker would have run over 15 weeks, use the geometric sequence formula and find the sum of the series.

Step-by-step explanation:

To find the total number of miles Parker would have run over 15 weeks, we will use the given information that Parker runs 7 miles in the first week and increases the number of miles he runs by 10% each week. We can set up a geometric sequence to represent the number of miles Parker runs each week:

The first term, a1, is 7 miles.

The common ratio, r, is 1 + 10% = 1.1 (since Parker increases his running distance by 10% each week).

Thus, we can use the formula for the sum of a geometric series to find the total number of miles Parker would have run:

Sn = a1(r^n - 1)/(r - 1)

Substituting the given values into the formula, we have:

S15 = 7(1.1^15 - 1)/(1.1 - 1)

Using a calculator to evaluate this expression, we find that Parker would have run approximately 194 miles.