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.

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.

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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

Related Questions

The sum of three consecutive terms of an A.P. is 21 and the sum of their squares is 165. Find these terms.

The angles of a quadrilateral are in A.P. with common difference 20°. Find its angles.

Split 207 into three parts such that these parts are in A.P. and the product of the two smaller parts is 4623.