If A₁,

As A₁ and A₂ are A.M between a and b

∴ we can write a,A₁,A₂,b

Let the first term of AP be a and the common difference be d.

∴ A₁ = a+d, A₂ = a+2d , b =a+3d

As G₁ and G₂ are G.M between a and b

∴ we can write a,G₁,G₂,b

Let the first term of AP be a and the common ratio be r.

∴ G₁ = aR, G₂ = ar² , b =ar³

∴

⇒

⇒