SOLUTION: In an A.P, the sum of three positive consecutive numbers is 21. The sum of their squares is 155.Find the numbers

Let x be the middle term of the AP (the second term) and d be the common difference.

Then the three terms are x-d, x, and x+d, and their sum is 3x = 21 --->  x  =  = 7. 

The second condition is 

 = 155,

which gives 

 = 155, 

147 + 2d^2 = 155,

2d^2 = 155 - 147 = 8,  --->  d^2 = 4  --->  d = +/-2.

So, the progression is  5, 7, 9  or  9, 7, 5.

Answer. {5, 7, 9}  or  {9, 7, 5}.