Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.
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Question

Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.

KnowledgeBoat · Accepted Answer

Let the four terms of A.P. are (a - 3d), (a - d), (a + d), (a + 3d). According to question, ⇒ a - 3d + a - d + a + d + a + 3d = 96 ⇒ 4a = 96 ⇒ a = 24. So, terms are, 24 - 3d, 24 - d, 24 + d, 24 + 3d. Given, ratio between product of their means to product of their extremes is 15 : 7. Let d = 6, Terms = (a - 3d), (a - d), (a + d), (a + 3d) = (24 - 3 × 6), (24 - 6), (24 + 6), (24 + 3 × 6) = 6, 18, 30, 42. Let d = -6, Terms = (a - 3d), (a - d), (a + d), (a + 3d) = (24 - 3 × -6), (24 - (-6)), (24 + (-6)), (24 + 3 × -6) = 42, 30, 18, 6. Hence, four parts of 96 are 6, 18, 30, 42 or 42, 30, 18, 6.

Mathematics

Divide 96 into four parts which are in A.P. and the ratio between product of their means to product of their extremes is 15 : 7.

AP

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