In which of the following situations,does the | vedclass

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(B) Let the initial volume of air in a cylinder be $V$ liters. In each stroke,the vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylind

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No,it does not form an arithmetic progression because the difference between consecutive terms is not constant.

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(B) Let the initial volume of air in a cylinder be $V$ liters. In each stroke,the vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder. This means that after every stroke,the remaining air is $1 - \frac{1}{4} = \frac{3}{4}$ of the previous amount. Therefore,the sequence of volumes after each stroke is $V, \frac{3}{4}V, \left(\frac{3}{4}ight)^2 V, \left(\frac{3}{4}ight)^3 V, \dots$. To check if this is an arithmetic progression $(A.P.)$,we calculate the difference between consecutive terms: $d_1 = \frac{3}{4}V - V = -\frac{1}{4}V$ $d_2 = \left(\frac{3}{4}ight)^2 V - \frac{3}{4}V = \frac{9}{16}V - \frac{12}{16}V = -\frac{3}{16}V$. Since $d_1 
eq d_2$,the difference between consecutive terms is not constant. Thus,this list of numbers does not form an $A.P.$

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 $\frac{1}{4}$ of the air remaining in the cylinder at a time.

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