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 
of the air remaining in the cylinder at a time.
Let V be the initial volume of air that is present in the cylinder.
They have said that a vacuum removes 
of the air.
Let initial volume (v) = 1 litre
After first removal of air, the remaining will be V1
V1 = 1- 
⇒ 
Similarly,
In second attempt it removes 
of the 
air remaining.
That means they remove 
= 
of air.
So, V2 = 
- 
⇒ 
After third attempt V3 = 
of air will be remaining.
So, the series will be look like
1, 
, 
The above series is NOT looking like A.P.
∵ Their common difference is not same.
1