The best question from arithmetic progressions of class 10th math of exercise 5.1. I am not able to solve this question so please help me sir for solving this question In which of the following situations, does the list of numbers involved make as arithmetic progression and why?(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.

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# In which of the following situations, does the list of numbers involved make as arithmetic progression and why?(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. Q.1(2)

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Let the volume of air in a cylinder, initially, be

Vlitres.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 onClearly, 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.