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anonymous
 one year ago
Hello! I don't know why I am getting the wrong answer, please help!
10 .The first three terms of a geometric sequence are 100, 90 and 81.
(iv) After how many terms is the sum of the sequence greater than 99% of the sum to infinity.
I get 22. the answer according to the text book is 44. In a previous question it is shown that the r=9/10
anonymous
 one year ago
Hello! I don't know why I am getting the wrong answer, please help! 10 .The first three terms of a geometric sequence are 100, 90 and 81. (iv) After how many terms is the sum of the sequence greater than 99% of the sum to infinity. I get 22. the answer according to the text book is 44. In a previous question it is shown that the r=9/10

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh I forgot to mention the sum to infinity of the terms of the sequence is 1000

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2Did you figure out the general sequence yet using those terms given

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2oh ok, had to look what that meant, sum to infinity is the limit of that sequence

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2have you seen this before: \[S _{n} = \frac{ a _{1}(1r^n) }{ 1r }\] sum of n terms of geometric series

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2r = ratio of n+1 term to the nth term ... r = 90/100 = 81/90 = 0.9

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2since the terms are always getting smaller and smaller by that ratio,, eventually the thing will settle or 'converge' to a certain value, the farther out you go in the value of n, the closer the total will be to the limiting value of the series

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2since they just gave you the sum to infinity is 1000, 99% of that is 990 you want that series to total 990 or more and find out how many terms it takes, n

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2\[990=\frac{ 100(10.9^n )}{ 10.9 }\] solve

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2you see the value for n, round up to the next whole number, that is the number of terms to get to 990, or , 99% of 1000

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2i got 43.something, so 44 terms to get there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh I think I see. Thank you very much!

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2yes yes, if they dont give you a value for the limit or infinite sum, then you can find it by the first value in the sequence divided by (1  r) 100/(10.9) = 1000

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2if r is larger than 1, then the thing will not have an infinite sum or converging value as n goes to larger

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2in that case it just blows up since each term is larger than the last

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. Good to know. :) Thanks very much!
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