Problema Solution
The 'n'th '2n'th and '3n'th term of a GP are a,b and c respectively. Show that b is the Geometric mean of a and c
Answer provided by our tutors
Let first term = f
let ratio = r
'n'th term = f*r^(n-1)
'2n'th term = f*r^(2n-1)
'3n'th term = f*r^(3n-1)
geometric mean = square root ('n'th * '3n'th)
'n'th term * 3n'th term = f*r^(n-1) * f*r^(3n-1) = f^2*r^(4n-2)
geometric mean = square root(f^2*r^(4n-2)) = f*r^((4n-2)/2) = f*r^(2n-1) = '2n'th term
hence proved