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Exercise:5.1
Q.1. In which of the following situations, does the list of numbers
involved make as 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.
Solution:
⇨Fare for 1st Km = Rs 15
⇨Fare for 2nd Km = 15 + 8 = Rs 23
⇨Fare for 3rd Km = 23 + 8 = Rs 31
⇨Fare for 4th Km = 31 + 8 = Rs 39
⇨Similarly 47,55,63...................
This Forms an AP because the common difference is same for all.
(ii) The amount of air present in a cylinder when a vacuum pump removes 1/4
of the air remaining in the cylinder at a time.
Solution:
⇨Let us consider the initial volume of cylinder be 'V'
⇨Therefore after every stoke the volume of air remain will be
⇨ After 1st stoke volume remains = 
= 
⇨ After 2nd stoke volume remains = 
⇨The common difference (d) is note same for every next term therefore it
doesn't form an AP.
iii. The cost of digging a well after every meter of digging, when it costs
Rs 150 for the first meter and rises by Rs 50 for each subsequent meter.
Solution:
Cost for 1 meter digging = 150
Cost for 2 meter digging = 150 + 50 = 200
Cost for 3 meter digging = 200 + 50 = 250
Cost for 4 meter digging = 250 + 50 = 300
The common difference ,d = a2 - a1 is same for every next term. So it forms
an AP.