Question 1. 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 1/4 of the air remaining in the cylinder at a time.
Solution: Given: 1/4 air removes when inserting a vacuum pum.
Suppose, the total initial air present = 100 (A1)
Now,
Number of air present after ist vaccum pump= 100 - 1/4 × 100 = 25
= 100 - 25 = 75 (A2)
Number of air present after 2nd vaccum pump=75 - 1/4 × 75= 18.75
= 75 - 18.75 = 56.25 (A3)
To check,
Difference = A2 - A1
= 75 - 100
= -25
Difference = A3 - A2
= 56.25 - 75
= -18.75
Hence, it does not form an AP (Arithmetic Progression) because the difference is not same.
