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 ^ (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

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
I think the difference in your answers is due to the switched sign in the numerator of the sum formula.