Question

Find the geometric mean of the series:1,2,4,...,2^n

Answer 1

Solution

We know that geometric mean of 2 digits is

G.M of a and b = (a.b)½

G.M of the given series

1,2,4,8,16,........,2^n

G.M = (1.2.4.8.16...2^n)^1/n+1

G.M = (2^0.2¹.2².2³.2⁴....2^n)^1/n+1

G.M = (2^0+1+2+3+4+n)^1/n+1

G.M = ( 2^n(n+1)/2)^1/n+1

G.M = 2^n/2