There are four numbers. The first three make an arithmetic progression, and the last three make a geometric progression. The sum of first and last number is $37$. The sum of middle numbers is $36$. Find the numbers.
So I'm trying to solve this problem for about 2 hours now. I can't use any formulas because all I get $0=0$. I don't know all the terms in English so I'll just try to upload my notes here. Eh but it doesn't let me. At first i got that $a_1=-2d$, $d$ was $= -36$ so my numbers were $72$, $36$, $0$, $-35$. The problem is that last 3 numbers doesn't make a geometric progression.