Q : 1     In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?

             (i) The taxi fare after each km when the fare is  \small Rs\hspace{1mm}15  for the first km and \small Rs\hspace{1mm}8  for each additional  \small km.

Answers (1)

It is given that
Fare for  1^{st} \ km = Rs. 15
And after that \small Rs\hspace{1mm}8  for each additional  \small km
Now,
Fare for  2^{nd} \ km = Fare of first km + Additional fare for 1 km 
                               =  Rs. 15 + 8 = Rs 23

Fare for 3^{rd} \ km = Fare of first km + Fare of additional second km + Fare of additional third km 
                              = Rs. 23 + 8= Rs 31

Fare of n km =  15 + 8 \times (n - 1) 
( We multiplied by n - 1 because first km was fixed and for rest we are adding additional fare.

In this, each subsequent term is obtained by adding a fixed number (8) to the previous term.)

Now, we can clearly see that this is an A.P. with first term (a) = 15 and  common difference (d) = 8
 

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