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Divide 28 into four parts in A.P. so that ratio of the product

Question

Divide 28 into four parts in A.P. so that ratio of the product of first and third with the product of second and fourth is 8:15.Now find the largest term in those four terms ?

A

10

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Divide 28 into four parts in A.P. so that ratio of the product of first and third with the product of second and fourth is 8:15.Now find the largest term in those four terms ?

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Text solutionVerified

Here

4 a = 28

So

a = 7.

Also

\frac{( a - 3 d ) ( a + d )}{( a - d ) ( a + 3 d )} = \frac{8}{15}

15 [a^{2} - 3 d^{2} - 2 a d] = 8 [a^{2} - 3 d^{2} + 2 a d]

7 [a^{2} - 3 d^{2}] = 46 a d

7 (49 - 3 d^{2}) = 46 \times 7. d

49 - 3 d^{2} = 46 d

3 d^{2} + 46 d - 49 = 0

(d - 1) (3 d + 49) = 0

d = 1

Required numbers are

4, 6, 8, 10

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Question Text	Divide 28 into four parts in A.P. so that ratio of the product of first and third with the product of second and fourth is 8:15.Now find the largest term in those four terms ?
Answer Type	Text solution:1
Upvotes	150