Let four numbers, the first three of which are in turn equal ratio sequence, the last three of which are in turn equal difference sequence, and the sum of the first and last two terms is 14, and the sum of the middle two terms is 12

Let four numbers, the first three of which are in turn equal ratio sequence, the last three of which are in turn equal difference sequence, and the sum of the first and last two terms is 14, and the sum of the middle two terms is 12

If the first number is x, then the fourth number is 14-x;
If the third number is y, then the second number is 12-y, then:
(1) The first three numbers are in an equal proportion sequence
(12－y)²=xy
(2) The last three numbers form a sequence of arithmetic numbers
2y=(12－y)＋(14－x)
x＋3y=26
X = 26-3y
Substituting (1), we get the following result:
(12－y)²=y(26－3y)
4y²－50y＋144=0
2y²－25y＋72=0
Y = 8 or y = 9 / 2
Thus, the corresponding x = 2 or x = 25 / 2
Then the four numbers are:
2. 4, 8, 12 or 25 / 2, 15 / 2, 9 / 2, 3 / 2