Help geometric progression

[Robertwellson]

Can someone help me solve this? Geometric progression and show me the steps

A chemical reaction produces 25.6cm of chemical ' A ' in the first minute of the reaction. For each of the subsequent minute, the amount of chemical ' A ' produced reduce such that it form a geometric progression. Given that the total amount of chemical ' A ' produced if the reaction continue over a long period of time is 102.4cm

( a) Find the common ratio

( b) in which minute, the amount if chemical ' A ' produced is 8.1

Answer for a is 0.75

And b is 5

 

[Cubist]

I think you should be able to solve this yourself. Take a look at this wikipedia page, particularly the section on "Infinite geometric series". You need to look at the infinite series section because the question talks about the total amount produced after a "long period of time". Therefore we can assume the reaction has finished, and mathematically this happens in the limit as we let the number of minutes tend towards infinity. Can you say which equation you'd use from that webpage? Can you try plugging the numbers in to obtain the value for r?

 

[Robertwellson]

I think you should be able to solve this yourself. Take a look at this wikipedia page, particularly the section on "Infinite geometric series". You need to look at the infinite series section because the question talks about the total amount produced after a "long period of time". Therefore we can assume the reaction has finished, and mathematically this happens in the limit as we let the number of minutes tend towards infinity. Can you say which equation you'd use from that webpage? Can you try plugging the numbers in to obtain the value for r?

Thank you very much, I have solved it. I use the formula a/1-r = 102.4

 

[HallsofIvy]

I hope you actually used 1/(1- r)! a/1- r= a- r will give the wrong answer.