aweller3898
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D'Andre has decided that he needs to get more exercise, so he is building a running regimen for himself. He decides that, beginning on Sunday, he'll run 10 feet. On each subsequent day, he'll double the distance he ran the previous day. So he'll run 20 feet on Monday, 40 feet on Tuesday, and so on. His Track coach (who also happens to be his math teacher) told D'Andre that he won't be able to keep to his plan for very long, but D'Andre is determined to make it work for at least two weeks.
 
A.) according to his plan, how far will he have to run on the 14th day. Give answer in miles.

B.) if he sticks to his plan, how far will he have run in those 2 weeks.

Respuesta :

ilebeck66
A. 81920 feet, or 15.5 miles.

He will have run 163850 feet. 

The distance ran in each day is in GP. That is [tex] 10,20,40,80,.... [/tex].

The n-th term of a GP is [tex] a_n=ar^{n-1} [/tex].

The sum of first n-terms of the GP is [tex] S_n=\frac{a(r^n-1)}{r-1} [/tex].

Where [tex] a [/tex] first term and [tex] r [/tex] common ratio.

Here [tex] a=10,r=2 [/tex]

a) The distance ran on the 14th day is [tex] a_{14}=10(2^{14-1})=81,920\;miles [/tex]

b) The total distance ran in 2 weeks is

[tex] S_{14}=\frac{10(2^{14}-1)}{2-1}=163,830\;miles [/tex]

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