CGPET 2015 Solved Paper

Given that, a, b and c are in Hp.
∴ Harmonic mean of a and c and c is b.
and geomatric mean of a and c is √ac.
∵ Geomatric mean > Harmonic mean
⇒ √ac>b ....(i)
Now, for the positive numbers an and cn, we have
Geomatric mean = √an.cn
and arithmetic mean =

an+cn

2

∵ AM > GM
∴

an+cn

2

>√an.cn
⇒ an+cn>2√an.cn
⇒ an+cn>2(√ac)n>2bn [using Eq. (i)]
⇒ an+cn>2bn