If the `4^(t h)`, `10^(t h)`and `16^(t h)`terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Answer

N/a

Explanation

Let first term be 'a' and common difference be 'r' of G.P.
`:. a_(4)=ar^(3),a_(10)=ar^(9) and a_(16)=ar^(15)`
Given that, `ar^(3)=x ……(1),ar^(9)=y`….(2)
and `ar^(15)=z`
From equation (1) and (3) , `xz=ar^(3)xxar^(15)`
`=a^(2)r^(18)=(ar^(9))^(2)`
`impliesxz=y^(2)`[From equation (2)]
`implies x,y,z` are in G.P Hence Proved