A) an AP
B) a GP
C) an HP
D) none of these
Correct Answer: B
Solution :
\[\frac{1}{2y}-\frac{1}{x+y}=\frac{1}{y+z}-\frac{1}{2y}\] |
\[\Rightarrow \] \[\frac{(x+y)-2y}{(x+y)}=\frac{2y-(y+z)}{y+z}\] |
\[\frac{x-y}{x+y}=\frac{y-z}{y+z}\] |
\[\Rightarrow \] \[xy+xz-{{y}^{2}}-yz=xy+{{y}^{2}}-xz-yz\] |
\[\Rightarrow \] \[{{y}^{2}}=xz\] |
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