The Question is from NCERT book of Class 10th on Page: 99 Exercise 5.1 Question no. 1 (ii). Find wether the following question is an A.P or Not? Give Solution.
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. Find whether this forms an A.P or not.
Let’s take the volume of air in the cylinder be ‘ V ‘.
In each time , the pump removes 1/4th of air in the cylinder at that a time.
After every stroke, 1-1/4 = 3/4th part of air remains.
Therefore, volumes will be V, 3V/4 , (3V/4)2 , (3V/4)3…and so on
We can see the adjacent terms of the series does not have any common difference between them. Thus, this series is not an A.P.