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If a b c are in harmonic progression show that a-b/b-c= a/c

If a b c are in harmonic progression show that a-b/b-c= a/c

Grade:11

2 Answers

User
6 Points
7 years ago
a, b, c are in HP
 
so 1/a, 1/b, 1/c are in AP.
thus 1/b – 1/a = 1/c – 1/b
=> (a – b) / ab = (b – c) / bc
=> (a – b) / (b – c) = ab / bc
=> (a – b) / (b – c) = a / c
anu anu30
26 Points
2 years ago
Find seven numbers A1,A2,...,A7 so that the sequence 4, A1,A2,...,A7, 7 is in arithmetic progression and also 4 numbers G1,G2, G3,G4,3/8 is in geometric progression

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