We need to find whether the situation given below makes an arithmetic progression and why?

  • 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.

I hope you can understand what I'm asking. please explain to me the answer


SARAHann  Mar 15, 2017

Yes it does you could even make the arithmetic equation of this. Say you have a volume of 5 (units) in the cylinder...

if you keep taking down the volume by 1/4 then it decreases by a common amount each time.


l'll even write out a sequence.


5, 19/4, 18/4, 17/4...


l'm sure you can figure the arithmetic for this, if not, let me know c:

HighSchoolCalculus  Mar 15, 2017

Oh but my school reader says that it doesn't form an A.P

Then how is it forming an A.P?indecision

SARAHann  Mar 16, 2017

Note that this forms a geometric progression, not an arithmetic one.....the amount that reamins each time is (/3/4) of the previous amount.....a common ratio...


We start with 5 units.....removing 1/4  of the air means that 5(3/4) = 15/4 units remain

Then....removing (1/4) of this means that  (15/4)(3/4) = 45/16 units remain....etc.



cool cool cool

CPhill  Mar 15, 2017

Well the rate that it changes at never accelerates so takes the remaining air as show in my arithmetic above.

HighSchoolCalculus  Mar 15, 2017

nvm l see it.

HighSchoolCalculus  Mar 15, 2017

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