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Question 1 (ii)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(ii) The amount of air present in a cylinder when a vacuum pump removes 14 of the air remaining in the cylinder at a time.


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Solution

Let us assume, initial quantity of air = V

Therefore, quantity removed in the first step = V × 14

Quantity remaining after the first step

= VV4 = 3V4

Quantity removed in the second step = 3V4 × 14

= 3V16

Quantity remaining after the second step

= 3V4 - 3V16 = 9V16

Quantity remaining after each step follows the trend:

V,3V4,9V16,...

Here each subsequent term is not obtained by adding a fixed number to the previous term.

Hence, it is not an AP.


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