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

Thanks!

SARAHann
Mar 15, 2017

#1**0 **

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

#2**0 **

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.

CPhill
Mar 15, 2017

#3**0 **

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

HighSchoolCalculus
Mar 15, 2017