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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
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5+0 Answers

 #1
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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
 #5
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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
 #2
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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
 #3
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Well the rate that it changes at never accelerates so takes the remaining air as show in my arithmetic above.

HighSchoolCalculus  Mar 15, 2017
 #4
avatar+1477 
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nvm l see it.

HighSchoolCalculus  Mar 15, 2017

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