(i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.
(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 (i):
The given condition can be written as;
Fare of taxi for 1 km = 15
Fare of taxi for first 2 kms = 15+8 = 23
Fare of taxi for first 3 kms = 23+8 = 31
Fare of taxi for first 4 kms = 31+8 = 39
And so on……
As a result, 15, 23, 31, 39… creates an A.P. because each subsequent phrase is 8 more than the previous one.
Solution(ii):
Let V litres be the initial volume of air in a cylinder.
The vacuum pump removes 1/4th of the air in the cylinder at a time with each stroke. Or, to put it another way, 1-1/4 = 3/4th of the air will remain after each stroke.
Therefore, the volumes will be V, 3V/4 , (3V/4)2 , (3V/4)3…and so on respectively.
Clearly, as we can see, the neighboring terms in this series do not have a common difference. As a result, this is not an A.P.