If the product of three terms of a G.P is 216 and the sum of their products taken in pairs is 156 then the greatest term is

Let the terms are ar,(a),(ar) Given that ar( a )(ar)=216→a=6 given that ar⋅a+(a )(ar) +(ar⋅a/r)=156 →a21r+r+1=156 since a=6⇒3r2−10r+3=0→r=3 or 1/3 ∴ the terms are 2,6,18∴ the greatest term is 18