Question

4 number are in AP the sum of stream Is 10 and product of the mean is 24 find the number

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Answer 1

Take the four numbers as (a-3d),(a-d),(a+d),(a+3d) in AP with common difference as 2d. Now given that Sum of four numbers = 96 i.e (a-3d)+(a-d)+(a+d)+(a+3d) = 96 => 4a = 96 => a = 24 ----------(1) Now to find d use the other condition. i.e Product of means/Product of Extremes = 35/27 => (a-d)(a+d) / (a-3d)(a+3d) = 35/27 => a2 - d2 / a2 -9d2 = 35/27 ---------------(2) Now find the value of d using equation (1) and (2) You will get d = 4 So the four numbers are: a-3d = 24-3*4 = 12 a-d = 24 - 4 = 20 a+d = 24+4 = 28 a+3d = 24+12 = 36 Hence the four numbers are 12,20,28,36Read more on Sarthaks.com - https://www.sarthaks.com/438/the-sum-four-numbers-that-the-product-the-means-product-the-extremes-then-find-the-numbers