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Arithmetic Progressions
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30/05/2021 12:22 pm
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In which of the following situations, does the list of numbers involved make an arithmetic progression and why?
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.
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30/05/2021 12:23 pm
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.
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.