SOLUTION: The sum of three numbers in arithmetic sequence is 24 . If the first number is decreased by 1 , and the second is decreased by 2 , the three numbers will now be in geometric sequ

Question 472701: The sum of three numbers in arithmetic sequence is 24 . If the first number is decreased by 1 , and the second is decreased by 2 , the three numbers will now be in geometric sequence. Use algebra to SOLVE for the three numbers (no guessing and testing).
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let a-k, a, a+k be the three numbers which sum up to 24. It should appear evident that a = 8.

So our numbers are 8-k, 8, and 8+k. We want 7-k, 6, 8+k to be in a geometric progression. We know that the ratio between successive terms is constant, so

k = 4 or k = -5. Hence the sequences are 4,8,12 and 13,8,3 (both work).
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