There are four numbers in the equal ratio sequence. Subtract 1,1,4,13 from these four numbers respectively, and then they will become the equal difference sequence again. Find these four numbers

There are four numbers in the equal ratio sequence. Subtract 1,1,4,13 from these four numbers respectively, and then they will become the equal difference sequence again. Find these four numbers

Let the first number be m and the common ratio be K, then the four numbers are
m
mk
mk^2
mk^3
Subtract 1,1,4,13 from these four numbers, and the new number is
m-1
mk-1
mk^2-4
mk^3-13
They form an arithmetic sequence, and there are two
(mk^3-13)-(mk^2-4)=(mk^2-4)-(mk-1)=(mk-1)-(m-1)
The results are as follows
mk^3-mk^2-9=mk^2-mk-3=mk-m
mk^2-mk-3=mk-m
k(mk-m)-3=mk-m
(k-1)(mk-m)=3
M (k-1) (k-1) = 3
mk^3-mk^2-9=mk-m
k^2(mk-m)-9=mk-m
M (k ^ 2-1) (k-1) = 9. Formula B
Substituting formula a into formula B, we get K + 1 = 3, k = 2, M = 3
What are the four numbers
three
six
twelve
twenty-four