Question -
Answer -
Given:
a, b and c are in GP
b2┬а=ac {property of geometric mean}
Apply log on bothsides with base m
logm┬аb2┬а=logm┬аac
logm┬аb2┬а=logm┬аa + logm┬аc {using property of log}
2logm┬аb= logm┬аa + logm┬аc
2/logb┬аm= 1/loga┬аm + 1/logc┬аm
тИ┤ 1/loga┬аm, 1/logb┬аm, 1/logc┬аm are in A.P.