CBSE Class 11-science - Relation Between AM and GM Videos
Relationship between A.M. and G.M.
This video explains the geometric Mean of two numbers and inserting numbers between any two numbers such that the sequence is a GP and establish the relation between AM and GM.
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More on Arthmetic mean of two numbers
- G1, G2, …, Gn are n geometric means between a and b. Find common ratio and (r + 1)th term of this GP (r < n).
- Find three geometric means between the numbers 3 and 48.
- Find the numbers whose arithmetic mean is 82 and geometric mean is 18.
- Find the sum of the series 3 + 9 + 27 + ……+ 6561.
- The A. M. between two positive numbers a and b is twice the G. M. between them. Find the ratio of the numbers.
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If a, b, c, d are in G.P., then prove that
are in G.P.
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If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that
.
- Find two positive numbers whose difference is 12 and whose AM exceeds GM by 2.
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Let ‘a’ be the AM and b & c be two GM’s between two any positive numbers. Then prove that
.
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Find n such that
may be the G.M. between positive numbers a and b.
