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Find three numbers in an arithmetic sequence, where the sum of the second and third is 12, and the product of the first and second is 5. 

 Nov 14, 2020
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F+D+F+2D = 12
F*(F+D)     = 5, solve for F, D


F = sqrt(51) - 6 - This is the first term.    D = -2/3 (sqrt(51) - 12) - This is the common difference.

 

The sequence is:
sqrt(51) - 6,    1/3 (6 + sqrt(51)),  1/3 (30 - sqrt(51)), 18 - sqrt(51)......etc.

 

OR:   1.141428,    4.380476,    7.619524,    10.858572....etc.

 Nov 15, 2020

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