A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance trav

Question

2 years ago

12

eled is 56.923 miles. Part A: How many miles did the hiker travel on the first day

1 answer:

Anastaziya [24] · Answer 1 · 2023-01-31T22:58:01+03:00

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.