# Hiking trip

Rosie went on a hiking trip. The first day she walked 18kilometers. Each day since she walked 90 percent of what she walked the day before. What is the total distance Rosie has traveled by the end of the 10th day?

Correct result:

x =  117 km

#### Solution:

$a_{1}=18 \ \text{km} \ \\ q=90 \%=\dfrac{ 90 }{ 100 }=0.9 \ \\ \ \\ a_{2}=a_{1} \cdot \ q=18 \cdot \ 0.9=\dfrac{ 81 }{ 5 }=16.2 \ \text{km} \ \\ a_{3}=a_{2} \cdot \ q=16.2 \cdot \ 0.9=\dfrac{ 729 }{ 50 }=14.58 \ \text{km} \ \\ ... \ \\ n=10 \ \\ \ \\ x=a_{1} \cdot \ \dfrac{ q^n-1 }{ q-1 }=18 \cdot \ \dfrac{ 0.9^{10}-1 }{ 0.9-1 }=117 \ \text{km}$

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