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Trying a progression of 1 gives

x+(x+1)+(x+2)

3x+3=12

x=3

33+43+53 = 216 Nope.

Trying a progression of 2 gives

x+(x+2)+(x+4)

3x+6=12

x=2

23+43+63 = 287 Still nope.

Trying a progression of 3 gives

x+(x+3)+(x+6)=12

3x+9 = 12

3x=3

x=1

13+43+73= 1 + 64 + 343 = 408 ■

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Q: The sum of three numbers in arithmetic progression is 12 and the sum of their cubes is 408the numbers are are?
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