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
(8+k) = -k^2 -k + 56)
k = 4 or k = -5. Hence the sequences are 4,8,12 and 13,8,3 (both work).
|
|
|
