Is this a geometric or arithmetic sequence

G

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A hiker walks 36 km on the first day and 2/3 that distance on the second. Everyday thereafter she walks 2/3 of the distance she walked on the day before. Will the hiker cover the distance of 100km to complete the walk and on what day will she complete the task?
 
An arithmetic series is additive!
A geometric series is multiplicative!
Which one of these operations does this problem require?
 
This is a geometric series.

She walks 36 the first day, 24 the 2nd day, 16 the third day and so on.

The partial sum of a geometric series is given by:

\(\displaystyle \L\\S_{n}=a_{1}(\frac{1-r^{n}}{1-r})\)

\(\displaystyle \L\\100=36\frac{1-(\frac{2}{3})^{n}}{1-(\frac{2}{3})}\)

Now, can you solve for n?.
 
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