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.
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.