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......an are non-zero positive numbers then their G.M (G) is provided by
G = (a1a2a3......an)1/n. If G1, G2,.....Gn are n geometric denotes between a and b then
a, G1, G2, ...., Gn, b may be a G.P. Here b = a rn + 1
![1636_Geometric Means.png](https://www.expertsmind.com/../CMSImages/1636_Geometric Means.png)
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 ax = by = cz and x, y, z are in G.P., prove that logb a = logc b
Solution: Shown as, ax = by = cz = k (say)
Taking logarithm, we have x log a = y log b = z log c = log k
![1813_Geometric Means1.png](https://www.expertsmind.com/../CMSImages/1813_Geometric Means1.png)
since x, y, z are in GP. y/x=z/y
![69_Geometric Means2.png](https://www.expertsmind.com/CMSImages/69_Geometric%20Means2.png)
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