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Geometric Mean is considered one of the most asked concept.
16 Questions around this concept.
Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of and
if is 4:5 then a:b can be:
For any three positive real numbers a, b and c, 9(25a2+b2)+25(c2−3ac)=15b(3a+c). Then:
If three terms are in G.P., then the middle term is called the Geometric Mean (G.M.) of the other two numbers. So if, a, b and c are in G.P., then b is GM of a and c,
If are n positive numbers, then the Geometric Mean of these numbers is given by
If a and b are two numbers and G is the GM of a and b. Then, a, G, b are in geometric progression.
Hence, .
Insertion of n-Geometric Mean Between a and b
Let be n geometric mean between two numbers a and b. Then,
is an G.P. Clearly, this G.P. contains n + 2 terms.
Important Property of GM
The product of n geometric mean between a and b is equal to the nth power of a single geometric mean between a and b.
If a and b are two numbers and are n-geometric mean between a and b, then
will be in geometric progression.
So, Product of n-G.M’s between a and b is
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Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra
Page No. : 5.12
Line : 27
Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra
Page No. : 5.12
Line : 39
July 04, 2019
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