SOLUTION: I don't understand this q 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

Question 1188914: I don't understand this q
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.
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

My guess is that it is the recursive formula you don't understand. I will explain that; then you can answer the questions.

If you then still need more help, re-post the question telling us WHAT it is about the problem that you don't understand.

The recursive formula is

tn = tn-1 + 0.75; t1 =8

I much prefer to write it as a function, like this:

t(n) = t(n-1)+0.75; t(1) = 8

In that form, t is the total taxi fare and n is the number of kilometers traveled. The recursive formula then says two things:

(1) The cost for traveling n kilometers is the cost for traveling (n-1) kilometers, plus 75 cents -- in other words, each additional kilometer costs 75 cents more; and

(2) The cost of traveling 1 kilometer is $8

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