In one city, a taxi fare includes an initial fixed charge, plus a charge based on each kilometre travelled. The possible fares charged, in dollars, in this city, can be represented by the recursion formula
tₙ = tₙ₋₁ + 0.75; t₁ = 8
a) What is the initial fixed charge?
b) What is the charge per kilometre travelled?
c) Is this an arithmetic or geometric sequence?
d) Find the general term of the sequence.
e) Calculate the fare for a 15 km trip.
a) The initial fixed charge is \(t_1 = 8\).
b) Charge per kilometre travelled is 0.75, because for each extra kilometer, the price is increased by 0.75, as described by the recursive formula.
c) This is an arithmetic sequence, since each term is 0.75 more than the previous one.
d) The general term of an arithmetic sequence is \(a + (n - 1)d\), where a is the first term and d is the common difference. Can you find those numbers and substitute into the expression? Don't forget to simplify the result.
e) After you have done d), substitute n = 16 into the expression also.