Find x for Geometric Progression: Solve with Step-by-Step Explanation

In summary, the value of x that forms a geometric progression for the sequence $x-1, 3x+4, 6x+8$ is -6.
  • #1
Fernando Revilla
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I quote a question from Yahoo! Answers

Find the value of x such that the following sequence forms a geometric progression...?
x-1, 3x+4, 6x+8...so i am suppose to solve this by this rule: a,b,c then b^2=ac but I am just going around in circles because i have no idea how to get an answer, my textbook says the answer is -6, but i want to know the working out...any answers appreciated!
thanks in advance:)

I have given a link to the topic there so the OP can see my response.
 
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  • #2
The sequence $x-1, 3x+4, 6x+8$ forms a a geometric progression if and only if:
$$\frac{3x+4}{x-1}=\frac{6x+8}{3x+4}\text{ and } x-1\neq 0\text{ and }3x+4\neq 0$$
Solving the equation
$$3x^2+22x+24=0\Leftrightarrow\ldots \Leftrightarrow x=-6\text{ or }x=-4/3$$
But $x=-4/3$ is not a valid solution (satisfies $3x+4=0$), so the solution is $x=-6$.
 

FAQ: Find x for Geometric Progression: Solve with Step-by-Step Explanation

What is a geometric progression?

A geometric progression is a sequence of numbers where each term is found by multiplying the previous term by a fixed number. This fixed number is called the common ratio, denoted by r.

How do you find the value of x in a geometric progression?

To find the value of x in a geometric progression, you can use the formula x = a * r^(n-1), where a is the first term, r is the common ratio, and n is the position of the term you are trying to find. Alternatively, you can also use the formula x = a * r^n, where n is the number of terms in the sequence.

What is the step-by-step process for solving a geometric progression?

The first step is to determine the first term and the common ratio in the sequence. Then, you can use the formula x = a * r^(n-1) or x = a * r^n to find the value of x in the sequence. Finally, you can check your answer by plugging in the value of x into the original sequence to see if it follows the geometric progression pattern.

Can you provide an example of solving a geometric progression for x?

Sure, let's say we have a geometric progression with a first term of 3 and a common ratio of 2. If we want to find the value of x in the 5th term, we can use the formula x = 3 * 2^(5-1) = 3 * 2^4 = 48. This means that the 5th term in the sequence is 48.

Are there any special cases to consider when solving a geometric progression for x?

Yes, there are a few special cases to consider. First, if the common ratio is 1, then the sequence is not geometric and there is no specific value for x. Second, if the common ratio is 0, then all of the terms in the sequence will be 0, making it impossible to find a specific value for x. Lastly, if the common ratio is a negative number, the sequence will alternate between positive and negative values, so you will need to be careful when finding the value of x.

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