If A1 and A2 be two AM 's and G1 and G2 be GM 's between 'a' and 'b', then find the value of (A1+A2) / ( G1*G2 ) !!thanks in advance !

A1 , A2 are inserted bw a,b ...

total terms now are 4 ...

let common difference is d then

a+(n-1)d = b

a+(4-1)d = b

3d = b-a .................1

second term is A1 = a+d

third term is A2 = a+2d

A1+A2  = 2a+3d = 2a+b-a                        (by using 1)

                       =a+b

now if A1,A2 are Gm's bw a,b then

 ar^n-1 = b

 ar³ = b

  r³ = b/a    ............2

2nd term is A1 = ar

third term is A2 = ar²

A1A2 = a²r³ = ab              (by using 2)

now A1+A2/A1A2 = a+b/ab

approve if u like my ans

Approved