Question

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

Answer 1

117 km

Explanation:

Answer 2

`110.34\text{ km}`

Explanation:

GIVEN: Rosie went on a hiking trip. The first day she walked
`18` kilometers. Each day since, she walked
`90\%` of what she walked the day before.

TO FIND: What is the total distance Rosie has traveled by the end of the
`10th` day.

SOLUTION:

Rosie walked first day
`=18\text{ km}`

Rosie walked on second day
`=(90)/(100)*18\text{ km}=16.2\text{ km}`

Rosie walked on third day
`=(90)/(100)*16.2\text{ km}=14.58\text{ km}`

this forms a GP with first term
`18` and common ratio
`0.9`

General term of GP

`a_n=ar^(n-1)`

Sum of GP

`S_(10)=a((1-r^(n-1))/(1-r))`

`S_(10)=18((1-0.9^(10-1))/(1-0.9))`

`S_(10)=18((0.613)/(0.1))`

`S_(10)=18((0.613)/(0.1))`

`S_(10)=110.34\text{ km}`

Hence Rosie traveled total
`110.34\text{ km}`