KVPY Sample Paper KVPY Stream-SX Model Paper-24

If \[\frac{1}{x+y},\] \[\frac{1}{2y},\] \[\frac{1}{y+z}\] are three consecutive terms of an A.P., then x, y, z are three consecutive terms of -

A) an AP

B) a GP

C) an HP

D) none of these

Correct Answer: B

Solution :

\[\frac{1}{2y}-\frac{1}{x+y}=\frac{1}{y+z}-\frac{1}{2y}\] \[\Rightarrow \frac{(x+y)-2y}{(x+y)}=\frac{2y-(y+z)}{y+z}\]

\[\frac{x-y}{x+y}=\frac{y-z}{y+z}\] \[\Rightarrow xy+xz-{{y}^{2}}-yz=xy+{{y}^{2}}-xz-yz\] \[\Rightarrow {{y}^{2}}=xz\]