​ If A1, A2 be two AM’s and G1, G2 be two GM’s between a and b, then find the value of A1 + A2 / G1.G2 . ​

Question

If A₁, A₂ be two AM’s and G₁, G₂ be two GM’s between a and b, then find the value of \(\frac{A_1 + A_2}{G_1 G_2}\).

Answer 1

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