Answer:
The equestrian overbid the horse by $485.75.
It takes the workman 12 days.
Step-by-step explanation:
Each nail costs 2 times more than the previous nail. So this is a geometric sequence where the first term is 1 and the common ratio is 2.
a₁ = 1
r = 2
There are 5 nails per horseshoe, and 4 horseshoes on a horse, for a total of 20 nails. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
Plugging in values:
S = 1 (1 − 2²⁰) / (1 − 2)
S = 1,048,575
The nails cost 1,048,575 cents, or $10,485.75. This is more than the cost of the horse, so the equestrian did not make a good deal.
Like before, this is a geometric sequence where the first term is 1 and the common ratio is 2.
The sum of the first n terms is:
S = a₁ (1 − rⁿ) / (1 − r)
Plugging in values:
4095 = 1 (1 − 2ⁿ) / (1 − 2)
4095 = 2ⁿ − 1
4096 = 2ⁿ
n = 12
It takes the worker 12 days.
