Question 1140594
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The middle term (the 2-nd term) is one third of the sum, i.e. 24/3 = 8.


The first and the third terms then are  (8-d) and (8+d), where "d" is the common difference.


Then for "d" you have this equation


{{{(8-d)^2 + 8^2 + (8+d)^2}}} = 224.


Simplify and solve for d.


64 - 16d + d^2 + 64 + 64 + 16d + d^2 = 224


2d^2 = 224 - 64 - 64 - 64


2d^2 = 32  ====>  d^2 = 32/2 = 16  ====>  d = +/- {{{sqrt(16)}}} = +/- 4.


So, there are two such progressions:  one is for d = 4,  and the three terms are 4, 8 and 12.


The other is for d = -4, and the three terms are the same in the reversed order  12, 8 and 4.
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Solved.