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