A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance trav
eled is 56.923 miles. Part A: How many miles did the hiker travel on the first day
1 answer:
Answer:
6.0 miles
Step-by-step explanation:
The sequence of distances is a geometric sequence with first term a1 and common ratio (1 +10%) = 1.10. The sum of 7 terms of the sequence is ...
S7 = a1·(r^7 -1)/(r -1)
56.923 = a1·(1.1^7 -1)/(1.1 -1)
5.6923 = a1·0.9487171
Dividing by the coefficient of a1 gives its value:
5.6923/0.9487171 ≈ 5.999997 ≈ 6.000
The hiker traveled 6.0 miles on the first day.
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