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given that the pro:uct of is wo zeros is 1224. The sum of four consecutive numbers in an AP is 32 and the ratioofthe product offirst andla it tem to the product of two middleterms is 7:15. Find the num ers |
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Answer» Let the four consecutive numbers in AP be (a - 3d), (a - d), (a + d) and (a + 3d)Formula : an-a+(n-1) da-3d + a - d + a + d + a + 3d = 32a = 8 ......(1)Now, (a - 3d)(a + 3d)/(a - d)(a + d) = 7/1515(a^2 - 9d^2) = 7(a^2 - d^2)15a^2 - 135d^2= 7a^2 - 7d^28a^2 = 128d^2Putting the value of a = 8 in above we get.8(8)^2= 128d^2d^2= 512/128d = 2So, the four consecutive numbers are 8 - (3*2)8 - 6 = 28 - 2 = 68 + 2 = 108 + (3*2)8 + 6 = 14Four consecutive numbers are 2, 6, 10 and 14 |
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