SOLUTION: The first term of a geometric series are 1,x,y, and the first three terms of an arithmetic series are 1,x,-y. prove that x^2 + 2x -1 = 0. and hence find y, given that x is positiv

Question 732805: The first term of a geometric series are 1,x,y, and the first three terms of an arithmetic series are 1,x,-y. prove that x^2 + 2x -1 = 0. and hence find y, given that x is positive
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Geometric sequence must have a common ratio for each successive term.

.

Arithmetic sequence must have a common difference for each successive term.

.

There occur two different formulas for y. We equate them:

That proved!

Find x through either completing the square or, preferably, use solution to quadratic formula. OR ,
OR , and you can continue for finding y.
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