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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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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oh I forgot to mention the sum to infinity of the terms of the sequence is 1000
Did you figure out the general sequence yet using those terms given
oh ok, had to look what that meant, sum to infinity is the limit of that sequence

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Other answers:

have you seen this before: \[S _{n} = \frac{ a _{1}(1-r^n) }{ 1-r }\] sum of n terms of geometric series
r = ratio of n+1 term to the nth term ... r = 90/100 = 81/90 = 0.9
since 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
sorry back,
yeah 44 looks right
since 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
\[990=\frac{ 100(1-0.9^n )}{ 1-0.9 }\] solve
you 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
i got 43.something, so 44 terms to get there
Oh I think I see. Thank you very much!
yes 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/(1-0.9) = 1000
if r is larger than 1, then the thing will not have an infinite sum or converging value as n goes to larger
in that case it just blows up since each term is larger than the last
Ok. Good to know. :) Thanks very much!

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