Hiking trip

Rosie went on a hiking trip. On the first day, she walked 18 kilometers. Each day since she walked 90 percent of what she had walked the day before. What is the total distance Rosie has traveled by the end of the 10th day?
Please round your final answer to the nearest kilometer.

Correct answer:

x =  117 km

Step-by-step explanation:

$$\begin{gathered} a_1=18\text{km} \\ q=90\%=\frac{90}{100}=\frac{9}{10}=0.9 \\ {a}_2=a_1\cdot q=18\cdot \frac{9}{10}=\frac{18\cdot 9}{10}=\frac{162}{10}=\frac{81}{5}=16.2\text{km} \\ {a}_3=a_2\cdot q=\frac{81}{5}\cdot \frac{9}{10}=\frac{81\cdot 9}{5\cdot 10}=\frac{729}{50}=14.58\text{km} \\ \dots \\ n=10 \\ x=a_1\cdot \frac{q^n-1}{q-1}=18\cdot \frac{{\frac{9}{10}}^{10}-1}{\frac{9}{10}-1}=117\text{km} \end{gathered}$$

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