If a, b, c Are in H.P. Prove that 2a-b,b,2c-b are in G.P.— Find Relationship Between a, b, c
When a b c are in H.P. (harmonic progression), the reciprocals of a, b, and c are in arithmetic progression. This relationship helps derive connections between the variables.
Definition of H.P.
If a, b, c are in **Harmonic Progression (H.P.)**, then:
1/a, 1/b, 1/c are in A.P.
Condition for A.P. of Reciprocals
Since 1/a, 1/b, 1/c are in A.P., we have:
2(1/b) = 1/a + 1/c
Relationship Between a, b, c
Multiply both sides by abc:
2ac = bc + ab
⟹ 2ac = b(a + c)
⟹ b = 2ac / (a + c)
This formula is often used to simplify problems where variables are in harmonic progression.
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Keywords
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harmonic progression, sequence and series, a b c relationship, reciprocals, arithmetic progression, Class 11, Class 12, math notes, exam question, harmonic mean, algebra, aklearningnepal, education,If a, b, c Are in H.P. Prove that 2a-b,b,2c-b are in G.P.
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If a, b, c Are in H.P. Prove that 2a-b,b,2c-b are in G.P.
