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02112011  #1 
Join Date: Feb 2011
Posts: 1

Geometric Sequences
I have to find the sum of a sequence. They don't tell me until what term but they give me the term itself in the sequence, so:
1/3  1/9 + 1/27 ..... 1/729 So I did: 1/729 = 1/3 x 1/3 ^ (n1) And got: n = 6 Then: Sn = 1/3 (1 + 1/3 ^ 6) / (1 + 1/3) I get 365/1458 which is slightly different from what I get when I right all down and perform it "manually" (364/1458, thus, 182/729) and very different from the answer both in the book and what I got from a Geometric Sequence calculator online. Can anyone please help me? Thanks 
02182011  #2  
Join Date: Nov 2010
Posts: 36

Quote:
I think you got your answer right and the book has a misprint. Quite common in maths books. Anyway, have a look at the following: The sequence upto the 6th term is as follows: 1/3, 1/9 ,1/27, 1/81, 1/243, 1/729 I got these two extra terms just by using the previous term and mutiplying it by the common ratio as follows: 1st term = 1/3 2nd term = 1/3 * 1/3 = 1/9 3rd term = 1/9 * 1/3 = 1/27 4th term = 1/27 *  1/3 = 1/81 5th term = 1/81 * 1/3 = 1/243 6th term = 1/243 * 1/3 = 1/729 So adding the terms together gives the sum which equals 182/729. Now using formulae for a GP to find the nth term is as follows: nth term = a * r^(n1) where: a = first term = 1/3 r = common ratio = 1/3 n = number of the term we are trying to find we get term 6 = 1/3(1/3)^(61) = 1/729 Now the sum of n terms formula is: a * (1  r^n)/(1  r) where: a = first term = 1/3 r = common ratio = 1/3 n = number of terms we want to sum (in our case the 6th term) So by formula the 6th term of the above Geometic Progression can be found with: sum of the 6 terms = 1/3(1 (1/3)^6)) / (1  1/3) = 1/3 * 728/729/ (4/3) = 1/3 * 728/729 * 3/4 = 182/729 Hope this helps 

02182011  #3  
Join Date: Dec 2008
Posts: 249

Quote:
= 243/729  81/729 + 27/729  9/729 + 3/729  1/729 = 182/729 The sum of a geometric sequence is: Sn = a(1  r^n)/(1  r) where a = the first term and r = common ratio In this case a = 1/3 and r = 1/3 So Sn = 1/3 (1  (1/3) ^ 6) / (1  ( 1/3)) Sn = 1/3(1  (1/729)) / (1 + 1/3) Sn = 1/3(728/729) / (4/3) Sn = (1/3)(728/729)(3/4) = 728/(4 x 729) = 182/729 I think the difference in your answers is due to the switched sign in the numerator of the sum formula. 

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