Thread: Geometric and Arithmetic series question
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Old April 30th, 2008, 09:26 PM
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Quote:
Originally Posted by smplease View Post
The question is:

The numbers x, y, z are succesive terms of a G.S with the sum of the three terms equal to 9. When taken in the order y, x ,z the numbers form an A.S. Find the values of x, y, z?

G.S 9 = x(r^3-1)/(r-1)
A.S 9 =(3/2) * (2x + (3-1)*d

So I have that the sum of the G.S and A.S are equal and therefore I can say that the equations are equal to each other but i just don't know where to go from here or if I'm correct...

Thanks for any help you can give me
"The numbers x, y, z are succesive terms of a G.S ...." => y/x = z/y => y^2 = xz .... (1)

".... with the sum of the three terms equal to 9" => x + y + z = 9 .... (2)

"When taken in the order y, x ,z the numbers form an A.S." => x - y = z - x => 2x = y + z .... (3)

Solve equations (1), (2) and (3) simultaneously for x, y, z.
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