SOLUTION: For what values of x will (..., x+1, x+5, 3x+2, ...) be a geometric sequence?

It will be a geometric sequence with common ratio r if but only if,
BOTH of the following are true:

1. the second term x+5 is r times the first term x+1, that is,

      x+5 = r(x+1)

AND

2. the third term 3x+2 is r times the second term x+5, that is,

     3x+2 = r(x+5)

So we have the system of two equations in two unknowns x and r:



Solve the first equation for r:



Substitute that for r in the second equation:




Multiply both sides by (x+1)











Oh darn! That doesn't factor, so we must use the quadratic formula
(Are you sure you copied it right?)



with a=2, b=-5, c=-23









Edwin