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

In summary, Homework Statement:A word of advice here. Always check your calculations. 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.
  • #1
Jaco Viljoen
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9

Homework Statement


Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S
Determine x

Homework Equations


r=x/(x-2)=(x+6)/x

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
 
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  • #2
Jaco Viljoen said:

Homework Statement


Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S
Determine x

Homework Equations


r=x/x-2=x+6/x

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
-4x+12/4=0
x=-3
You might want to double check your algebra when solving for x.
 
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  • #3
@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.

Thank you for your input.
Jaco
 
  • #4
Jaco Viljoen said:

Homework Statement


Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S
Determine x

Homework Equations


r=x/x-2=x+6/x

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

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.
 
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  • #5
Thank you for pointing this out Ray,
I did pick up the error on the following statements before posting but have corrected these swell.
Does my answer make sense?

Thank you again.
 
  • #6
Jaco Viljoen said:
Does my answer make sense?

Thank you again.
What do you think?

Can you show that it does indeed make sense?
 
  • #7
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 [itex]3^0, 3^1, 3^2[/itex]. 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.
 
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  • #8
Jaco Viljoen said:
@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.

Thank you for your input.
Jaco
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.
 
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Likes Jaco Viljoen
  • #9
Thank you everyone,
I appreciate the help, distance learning has its downfall with math.
Have a great day.
 
  • #10
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
 

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

1. What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant value. This constant value is called the common ratio.

2. How do you determine the common ratio in a geometric sequence?

The common ratio in a geometric sequence can be found by dividing any term by the previous term. For example, in the sequence 2, 6, 18, 54, the common ratio would be 6/2 = 3.

3. What is the formula for finding a specific term in a geometric sequence?

The formula for finding the nth term in a geometric sequence is: an = a1 * rn-1, where an is the nth term, a1 is the first term, and r is the common ratio.

4. How do you determine if three numbers are sequential terms in a geometric sequence?

To determine if three numbers are sequential terms in a geometric sequence, you can check if the ratio of the second term to the first term is equal to the ratio of the third term to the second term. If they are equal, then the numbers are sequential terms in a geometric sequence.

5. Can a geometric sequence have negative common ratio?

Yes, a geometric sequence can have a negative common ratio. This means that the terms in the sequence are decreasing instead of increasing. For example, the sequence -3, 6, -12, 24 is a geometric sequence with a common ratio of -2.

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