If `a ,b ,c ,d` are four distinct positive numbers in G.P. then show that `a+d gt b+c dot`

Explanation

a,b,c,d are in G.P

so,`a/(r^2),a/r,ar.ar^2` are in G.P

`a+d=a/(r^2)+ar^2=a(1/(r^2)+r^2)`

`b+c=a/r+ar=a(1/r+r)`

so,`a(1/(r^2)+r^2)gta(1/r+r)`

Thus,`a+bgtb+c`