Question

In the sequence: x+4y ; 2y+2 ;x ;y-1, (consisting of 4 terms) the first three terms form an arithmetric progression, while the last three tern form a geometric sequence. Calculate the values of x and y. Answer(s) can be left in surd form.

Answer 1

"the first three terms form an arithmetric progression"
so....
2y+2 - (x+4y) = x - (2y+2)
which gives x = 2

"the last three tern form a geometric sequence"
so ...
x/(2y+2) = (y-1)/x , but we know x = 2

2/(2y+2) = (y-1)/2

I get y = ±√3