Geometric Series/Sequence word problem

[Lyphta]

okay... well i kinda got stuck on this question...

Every minute, a certain vacuum pump removes 1/4 of the air remaining in a closed container.

a. show that they amounts of air remaining in the container after each minute form a geometric sequence, and find the fraction of the original amount fremaining in the container after 5 minutes.

b. the total amount of air removed from the container after any given number of minutes is the sum of a geometric series. Find a1 and r for this series and use these values to find the fraction of the original amount of air that is removed in 5 minutes.

the formulas:
geometric sequence: an= a1(r)^n-1
geometric series: Sn=a1-a(r)^n/1-r
or Sn=a1-r(an)/1-r

thanks for helping in advanced.

 

[stapel]

Every minute, a certain vacuum pimp...

:shock:

Um... I'm gonna guess you mean "pump", okay?

a) How much are you starting with? One hundred percent of the original volume, or "1". How much is left after one minute? 1 - (1/4)(1) = 1 - 1/4 = 4/4 - 1/4 = 3/4. How much is left after two minutes? 3/4 - (1/4)(3/4) = 3/4 - 3/16 = 12/16 - 3/16 = 9/16. How much is left after three minutes? And so forth. Find the first six terms (the sixth being the amount left after five minutes), and show that these terms have a common ratio, so the sequence is geometric.

b) Follow the same process as above, noting that, in this case, you are finding how much was taken out, not how much is left. So, at minute 0 (when you start), you have no air taken out. After one minute (n = 1), you have 1/4 of the air taken out, leaving 3/4. After two minutes, you have (1/4)(3/4) = 3/16 taken out. And so forth.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.