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        riddles >> general problem-solving / chatting / whatever >> GP Problem
        
(Message started by: Sir Col on May 6^th, 2008, 2:48pm)

Title: GP Problem
Post by Sir Col on May 6^th, 2008, 2:48pm

Another mathematics teacher at my school brought a question she found in a textbook to my attention and I cannot see how it is supposed to be solved easily...

Quote:

The sum of the first four terms of a geometric series is 5468.75 and the first term is 2000. Find the value of the common ratio if all the terms are positive.

Apart from solving a cubic (or quartic) analytically, or even numerically, am I missing something obvious?

Title: Re: GP Problem
Post by towr on May 6^th, 2008, 3:18pm

Nothing obvious, but

[hide]1+x+x^2+x^3 = 5468.75/2000= 175/64
(1+x)(1+x^2)= 175/64
guess -> (4+y)(16+y^2) = 175, y=4x
175 = 7 * 25 => y = 3 => x = 3/4[/hide]

It shouldn't be hard to find a similar problem where this approach would utterly fail, I imagine. Of course, textbooks have the tendency towards simple answers. I'd expect a neat fraction, and so I found it.