SOLUTION: Given that {{{1/(y-x)}}} , {{{1/(2y)}}} and {{{1/(y-z)}}} are consecutive terms of an arithmetric progression, prove that x, y and z are consecutive terms of a geometric progressio

Question 1073135: Given that , and are consecutive terms of an arithmetric progression, prove that x, y and z are consecutive terms of a geometric progression
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
One nice thing about arithmetic progressions is that
if a, b, and c are three consecutive terms in an arithmetic progression (AP),
a + c = 2b (and if a + c =2b, a, b, and c form an AP).
That means that

Cancelling like terms,

One nice thing about geometric progressions is that
if x, y, and z are three consecutive terms in a geometric progression (GP),
, and if then x, y, and z form a GP,
and that is exactly what we found above.
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