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# Sequences

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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.

May 19, 2022

#1
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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.

May 19, 2022
edited by MaxWong  May 19, 2022
#2
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Thanks!

Would this be right for d?

8 + (n - 1)0.75

= 8 + 0.75n - 0.75

= 0.75n + 7.25

Is there a reason for e) I would substitute n = 16 for a 15km trip and not n = 15?

DumbDude05  May 22, 2022
edited by Guest  May 22, 2022