Question 399349
a  + d  =7 ==> d = 7  - a.
Now a(a+d)(a + 2d) = 280.
By substitution, 

a(a  +7 - a)(a + 14 - 2a) = 280
<==> 7a(14 - a) = 280
<==> a(14  -a) = 40
<==> {{{0 = a^2 - 14a + 40}}}
<==> (a - 4)(a - 10) = 0
==> a = 4, 10.
Two possible sequences arise, {4,7,10} and {10,7, 4}, which are essentially the same. Therefore the three numbers are 4,7, and 10.