Question

If odd number of G.M.s are inserted between two given quantities a and b, show that the middle G.M.=√(ab)​

Answer 1

Thus the middle G.M = √ ab

Step-by-step explanation:

a, g1, g2, g3 ----------- gn, gn+1, g2n -1, b

a & b ab = g1, g2n -1 = gn g2n .........= gn-1, gn+1 = gn^2

gn^2 = ab    ------(1)

Taking square root on both sides of the equation.

√ gn^2 = √ ab

gn = √ ab

Thus the middle G.M = √ ab