Thanks a lot mrfantastic!!! =)
But I got a similiar question which I can't solve:
The sum of the first 20 terms of a geometric series is 10 and the sum of the first 30 terms is 91, find the sum of the first 10 terms.
I divided S20 by S10 to eliminate 'a' so as to find 'r':
(r^30 -1) / (r^20 -1) = 91/10
Got to here but I am not sure how to continue. If I expand I will end up with this equation:
10r^30 - 91r^20 + 81 = 0
and the graph of this equation looks kind of weird.
But if I express in this form: 10(r^10)^3 - 91(r^10)^2 +81 = 0
I get r^10 = 9, 1, -9/10
Is there a better way to simplify so I can end up with a simple EQN like the previous question here: http://www.mathhelpforum.com/math-he...tml#post661852?
I think that the way the problem was presented,
you could try to find S10 from S30 and S20,
since the difference between these sums is 10 terms.
We can write 2 equations from the above
Hence
Also
Therefore, we have the equation
This leads to a quadratic equation
Since is an even power and hence positive, the negative solution for x is ruled out.
Finally
After seeing Archie Meade's post I found a mistake in my previous post. You cannot use all the three values you have obtained as I have mistakenly stated.
Case 1: Let,
When r=1;
But 'a' must have a unique value, so we cannot take r=1.
When r=-1;
But we know that, are not equal to zero. Hence we cannot take r=-1 either.
So cannot be taken.
Case 2: Let,
In this case r would be a complex value and obviously the sums would also be complex values which is again a contradiction.
Therefore we cannot take
The only solution that could be used is,