1. ## [SOLVED] common ratio

ok I thought I got this right but its not working "according to the answer"

If x - 2 , x + 4 , 5x + 2 are three consecutive terms in a geometric sequence, determine the numerical value(s) of the common ratio(s).

but if you plug that back in the -1 works but the 3 gives you
1,7,17?

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 and my ratios are -1 and 5 when I plug them back in.... whats goin on?

2. Hello, brentwoodbc!

If $x - 2 , x + 4 , 5x + 2$ 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 ${\color{blue}r}$

but if you plug that back in the -1 works
. . but the 3 gives you 1, 7, 17? . You're letting ${\color{blue}x = 3}$

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?

3. Originally Posted by brentwoodbc
ok I thought I got this right but its not working "according to the answer"

If x - 2 , x + 4 , 5x + 2 are three consecutive terms in a geometric sequence, determine the numerical value(s) of the common ratio(s).

but if you plug that back in the -1 works but the 3 gives you
1,7,17?

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 and my ratios are -1 and 5 when I plug them back in.... whats goin on?
If x= -1, then the three numbers are -1-2= -3, -1+ 4= 3, 5(-1)+ 2= -3 so your geometric sequence begins -3, 3, -3. The common ratio is -1.

If x= 5, then the three numbers are 5-2= 2, 5+ 4= 9, 5(5)+ 2= 27 so your geometric sequence begins 3, 9, 27. The common ratio is 3.

4. thanks I got my x/common ration mixed up...

5. thank you