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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 Rs 15 for the first km and Rs 8 for each additional km.

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)
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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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