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02-18-2011   #3
MAS1

Join Date: Dec 2008
Posts: 249

Quote:
 Originally Posted by Peter G 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 ^ (n-1) 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
1/3 - 1/9 + 1/27 - 1/81 + 1/243 - 1/729 ...
= 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