Show that a², b² and c² are in A.P., 1/b+c, 1/c+a and 1/a+b if are in A.P.

Question

KnowledgeBoat · Accepted Answer

Since are in A.P., ⇒ (b − a)(a + b) = (c − b)(b + c) ⇒ ab + b2 − a2 − ab = bc + c2 − b2 − bc ⇒ b2 − a2 = c2 − b2 ⇒ b2 − a2 = c2 − b2 We have, b2 − a2 = c2 − b2 Since consecutive differences are equal, Therefore, a2, b2, c2 are in A.P. Hence, a2, b2, c2 are in A.P.

Mathematics

Show that a², b² and c² are in A.P., 1/b+c, 1/c+a and 1/a+b if are in A.P.

AP

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Mathematics

Show that a², b² and c² are in A.P., 1/b+c, 1/c+a and 1/a+b if are in A.P.

AP

Related Questions

If pth term of an A.P. is q and its qth term is p, show that its (p + q)th term is zero.

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A man saved ₹ 7,65,000 in 10 years. In each year, after the first, he saved ₹ 6,000 more than he did in the preceding year. How much did he save in the first seven years?

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If S_n denotes the sum of first n terms of an A.P., prove that :
S₁₂ = 3(S₈ − S₄)