SOLUTION: Question: The sum of the first two terms of a decreasing geometric series is 5/4, and the sum to infinity is 9/4. Write the first three terms of the geometric series.
I solved i
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Question 1163948: Question: The sum of the first two terms of a decreasing geometric series is 5/4, and the sum to infinity is 9/4. Write the first three terms of the geometric series.
I solved it. I dont need the answer. It was tedious, which is ok if that is the way to do it. But I need to know whether I am making it tedious because the way I approached it and whether I am missing another easier way to solve it!
The way I solved it was:
a + ar = 5/4 (1)
a/(1-r) = 9/4 (2)
Subtracting (1) - (2) gave me ar^2 (the third term) = 3/2
Dividing (1)/(2) gave me r= +/- (2/3) and in turn plugging the values gave me a=3/4.
(Then I realized that there was no need for the tedious subtraction!!)
Also can I assume 'dividing the sum of a geometric series by its sum to infinity will always yield r^2 '
Thank you
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The 
th partial sum of a geometric sequence is given by:
}{\(1\,-\,r\))
Then, given that 
, dividing the partial sum by the infinite sum:
yields
Which is consistent with your calculations, that is you got 
from which you got 
using the partial sum 
.
John
My calculator said it, I believe it, that settles it
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