Geometric Means:

• If three terms are in G.P., then the middle term is known as the geometric mean (G.M.) between the two. So if a, b, c are in G.P. then b = √ac is the geometric mean of c and a.
• If a₁, a₂......a_n are non-zero positive numbers then their G.M (G) is provided by
  G = (a₁a₂a₃......a_n)^1/n. If G₁, G₂,.....G_n are n geometric denotes between a and b then
  a, G₁, G₂, ...., G_n, b may be a G.P. Here b = a r^{n + 1}

Problem: The third term of a G.P. is 7. Calculate the product of first five terms.

Solution:  Consider the terms be a/r²,a/r, a , ar, ar²          Þ a = 7.

                              The multiplication   = a⁵   = 7⁵.

Problem:  If a^x = b^y = c^z and x, y, z are in G.P., prove that log_b a = log_c b

Solution: Shown as, a^x = b^y = c^z = k (say)

                Taking logarithm, we have x log a = y log b = z log c = log k

                since x, y, z are in GP.  y/x=z/y 

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