Question

Find three consecutive nbees the sum of whose square is 302

Answer 1

Answer:

The mean of the three numbers is 30/3 = 10, but there are infinitely many arithmetic sequences of three numbers summing to 30.

If the common difference is d, then the sum of the squares of 10-d, 10, and 10+d will be 300 plus twice the square of the common difference.

e.g. if the sequence is 10, 10, 10, then the sum of squares is 300

If the sequence is 9, 10, 11, we get 302

If the sequence is 0, 10, 20, we get 500.

etc….

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