Suppose x-2, x and x+6 where are sequential terms in a geometric sequence

1. May 7, 2015

Jaco Viljoen

1. The problem statement, all variables and given/known data
Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S
Determine x

2. Relevant equations
r=x/(x-2)=(x+6)/x

3. The attempt at a solution
x/(x-2)=(x+6)/x cross multiply
x(x)=(x-2)(x+6)
x^2=x^2+4x-12
x^2-x^2+4x-12/4=0
4x=12
x=3

Last edited: May 7, 2015
2. May 7, 2015

SteamKing

Staff Emeritus
You might want to double check your algebra when solving for x.

3. May 7, 2015

Jaco Viljoen

@SteamKing I have corrected the -to+, am I doing the right thing?
I am quite rusty with math, I have started a degree towards civil engineering now at the age of 33, I last practiced math in 2000.

Jaco

4. May 7, 2015

Ray Vickson

Now is the time to learn to break bad habits: Never write something like x/x-2, because the means $\frac{x}{x} - 2 = 1 - 2 = -1$ when read using standard parsing rules for mathematical expressions. You want $\frac{x}{x-2}$, so you need parentheses, like this: x/(x-2). Similarly for your other expression x+6/x, which means $x + \frac{6}{x}$ as you have written it. You should write (x+6)/x.

5. May 7, 2015

Jaco Viljoen

Thank you for pointing this out Ray,
I did pick up the error on the following statements before posting but have corrected these swell.

Thank you again.

6. May 7, 2015

SammyS

Staff Emeritus
What do you think?

Can you show that it does indeed make sense?

7. May 7, 2015

HallsofIvy

Staff Emeritus
Apparently you have edited your original solution. You now have x= 3 in which case x- 2= 1, x= 3, and x+ 6= 9 so the sequence is 1, 3, 9 which is the same as $3^0, 3^1, 3^2$. Yes, that is a geometric sequence. With you original answer, which was apparently x= -3, x- 2= -5, x= -3, x+ 6= 3. The sequence -5, -3, 3 is NOT a geometric sequence.

Last edited: May 7, 2015
8. May 7, 2015

SteamKing

Staff Emeritus
Yes, your calculation is now correct.

A word of advice here. Always check your calculations. It's very easy for arithmetic mistakes to creep into a calculation. Making mistakes like this will be important to avoid later on in studying for your degree. Silly mistakes can cost you points on exams and assignments.

9. May 7, 2015

Jaco Viljoen

Thank you everyone,
I appreciate the help, distance learning has its downfall with math.
Have a great day.

10. May 7, 2015

Jaco Viljoen

a follow up question to this:
Suppose (x-2) is the 4th term, determine the first:
An=A1*34-1
(x-2)=A1*33
(x-2)=A*27
(x-2)=27A
A=(x-2)/(27)
A=1/27 (x-2) was determined in the previous answer as 1
=3-3