# 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