Question 637907
Let x be the first term and k be the common difference.
The three consecutive terms of the sequence are x, x + k, and x + 2k.
sum: 3x + 3k = 21 or x + k = 7 or k = 7 - x
product: x(x + k)(x + 2k) = 315, substitute k = 7 - x
         x(7)(14 - x) = 315, divide both sides by 7
         {{{x(14 - x)= 45}}} 
         {{{x^2 -14x + 45 = 0}}}
         {{{(x - 5)(x - 9) = 0}}}
If x = 5, then k =2 and the terms of the sequence are 5, 7, and 9.
If x = 9 then k = -2 and the terms of the sequence are 9, 7, and 5.

Answer: 5, 7, and 9.