Quote:

If $\displaystyle x - 2 , x + 4 , 5x + 2$ are three consecutive terms in a geometric sequence,

determine the numerical value(s) of the common ratio(s).

Correct answer is -1 and 3 . These are values of $\displaystyle {\color{blue}r}$

but if you plug that back in the -1 works

. . but the 3 gives you 1, 7, 17? . You're letting $\displaystyle {\color{blue}x = 3}$

I did 5x +2 over x+4 equal to x+4 over x-2

cross multilpied

solved for x by factoring and got -1,5 . . . . correct so far!

and my ratios are -1 and 5 when I plug them back in. . . . . How?