Question

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.​

Answer 1

$\huge \underline \mathbb {SOLUTION:-}$

Let the volume of air in a cylinder, initially, be V litres.

In each stroke, the vacuum pump removes 1/4th of air remaining in the cylinder at a time. Or we can say, after every stroke, 1-1/4 = 3/4th part of air will remain.

Therefore:

• Volumes will be V, 3V/4 , (3V/4)² , (3V/4)³…and so on

Clearly, We can see here, the adjacent terms of this series do not have the common difference between them. Therefore, this series is not an A.P.

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Answer 2

Let the volume of air in a cylinder, initially, be V litres.

In each stroke, the vacuum pump removes 1/4th of air remaining in the cylinder at a time. Or we can say, after every stroke, 1-1/4 = 3/4th part of air will remain.

Therefore, volumes will be V, 3V/4 , (3V/4)2 , (3V/4)3…and so on

Clearly, we can see here, the adjacent terms of this series do not have the common difference between them. Therefore, this series is not an A.P.