If $p,q$, and $r$ are terms of an arithmetic progression are also in a geometric progression, then find the common ratio of the geometric progression in terms of $p,q$, and $r$.
Find the common ratio of geometric progression
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algebra-precalculus
sequences-and-series
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0I also do not know if ([tag:sequences-and-series]) is the proper tag, but I think it's a better fit than ([tag:calculus]). If anyone has a better idea for a tag, feel free to change it. – 2012-02-24
1 Answers
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Hint: Let $p,q,r$ be the terms. Let $x$ be the ratio in the geometric progression, $y$ be the increment in the arithmetic progression. $x=\frac qp, y=q-p$ Then the terms are $p, px, px^2$ and also $p, p+y, p+2y$. Can find two equations for $x$ and $y$?
Added: You have $p+y=px, p+2y=px^2$. We have two equations in two unknowns if we regard $p$ as a parameter. Subtracting, $y=px^2-px$. Dividing, $x=\frac rq=\frac {p+2y}{p+y}$. I suspect the desired answer is the solution for $x$ of these two.
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0If p,q,r are adjacent ter$m$s, then the common ratio is $\$f$rac{p}{q}$. I suspect they need not be adjacent, and perhaps so$m$e information is missing from the problem... – 2012-02-24