Find three numbers in A.P. whose sum is 24 and whose product is 440.

Question

KnowledgeBoat · Accepted Answer

Let three numbers in A.P. be (a - d), a, (a + d). Sum = 24 ∴ a - d + a + a + d = 24 ⇒ 3a = 24 ⇒ a = 8. Product = 440 ⇒ (a - d)(a)(a + d) = 440 ⇒ (8 - d)(8)(8 + d) = 440 ⇒ (8 - d)(8 + d) = ⇒ 64 - d² = 55 ⇒ d² = 64 - 55 = 9 ⇒ d = ± 3 Let d = 3, A.P. = (8 - 3), 8, (8 + 3) = 5, 8, 11. Let d = -3, A.P. = (8 - (-3)), 8, (8 + (-3)) = 11, 8, 5. Hence, A.P. = 5, 8, 11 or 11, 8, 5.

Mathematics

Find three numbers in A.P. whose sum is 24 and whose product is 440.

AP

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Find three numbers in A.P. whose sum is 24 and whose product is 440.

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