Find three numbers in A.P., whose sum is 15 and the product is 80.

Question

KnowledgeBoat · Accepted Answer

Let the three numbers in the Arithmetic Progression (A.P.) be a - d, a, a + d. Given, The sum of the three numbers is 15. ⇒ a - d + a + a + d = 15 ⇒ 3a = 15 ⇒ a = ⇒ a = 5. The middle term of the A.P. is 5. Given, The product of the three numbers is 80. ⇒ (a - d)(a)(a + d) = 80 ⇒ (5 - d)(5)(5 + d) = 80 ⇒ (5 - d)(5 + d) = ⇒ (5 - d)(5 + d) = 16 ⇒ 52 - d2 = 16 ⇒ 25 - d2 = 16 ⇒ d2 = 25 - 16 ⇒ d2 = 9 ⇒ d = ⇒ d = 3 or d = -3. Case 1 : If a = 5 and d = 3 ⇒ a - d = 5 - 3 = 2 ⇒ a = 5 ⇒ a + d = 5 + 3 = 8. Case 2 : If a = 5 and d = -3 ⇒ a - d = 5 - (-3) = 8 ⇒ a = 5 ⇒ a + d = 5 + (-3) = 2. Hence, the numbers are 2, 5, 8.

Mathematics

Find three numbers in A.P., whose sum is 15 and the product is 80.

AP

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