If P R = 4 X − 2 PR = 4x - 2 PR = 4 X − 2 And R S = 3 X − 5 RS = 3x - 5 RS = 3 X − 5 , Which Expression Represents P S PS PS ?A. X − 7 X - 7 X − 7 B. X − 3 X - 3 X − 3 C. 7 X − 7 7x - 7 7 X − 7 D. 7 X + 3 7x + 3 7 X + 3

Introduction

In mathematics, a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this article, we will explore how to find the expression that represents the segment PS in a geometric sequence given the expressions for PR and RS.

Understanding the Problem

We are given two expressions:

• $PR = 4x - 2$
• $RS = 3x - 5$

Our goal is to find the expression that represents the segment PS.

Breaking Down the Problem

To find the expression for PS, we need to understand the relationship between PR, RS, and PS. Since PR and RS are adjacent segments in a geometric sequence, we can use the concept of a common ratio to find the expression for PS.

Finding the Common Ratio

The common ratio (r) is the ratio of any two adjacent terms in a geometric sequence. In this case, we can find the common ratio by dividing RS by PR:

$$r = \frac{RS}{PR} = \frac{3x - 5}{4x - 2}$$

Simplifying the Common Ratio

To simplify the common ratio, we can multiply both the numerator and denominator by 2:

$$r = \frac{(3x - 5)(2)}{(4x - 2)(2)} = \frac{6x - 10}{8x - 4}$$

Finding the Expression for PS

Now that we have the common ratio, we can find the expression for PS by multiplying PR by the common ratio:

$$PS = PR \cdot r = (4x - 2) \cdot \frac{6x - 10}{8x - 4}$$

Simplifying the Expression for PS

To simplify the expression for PS, we can multiply the numerator and denominator by 4:

$$PS = (4x - 2) \cdot \frac{(6x - 10)(4)}{(8x - 4)(4)} = \frac{(4x - 2)(6x - 10)(4)}{(8x - 4)(4)}$$

Further Simplification

We can simplify the expression further by multiplying the numerator and denominator by 2:

$$PS = \frac{(4x - 2)(6x - 10)(2)}{(8x - 4)(2)} = \frac{(8x - 4)(6x - 10)}{(8x - 4)}$$

Final Simplification

Now we can cancel out the common factor (8x - 4) in the numerator and denominator:

$$PS = 6x - 10$$

Conclusion

In this article, we have shown how to find the expression that represents the segment PS in a geometric sequence given the expressions for PR and RS. We used the concept of a common ratio to find the expression for PS and simplified it to its final form.

Answer

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Introduction

In our previous article, we explored how to find the expression that represents the segment PS in a geometric sequence given the expressions for PR and RS. In this article, we will answer some frequently asked questions related to solving for PS in a geometric sequence.

Q: What is a geometric sequence?

A: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Q: How do I find the common ratio in a geometric sequence?

A: To find the common ratio, you can divide any two adjacent terms in the sequence. For example, if you have the expressions PR and RS, you can find the common ratio by dividing RS by PR:

$$r = \frac{RS}{PR} = \frac{3x - 5}{4x - 2}$$

Q: How do I simplify the common ratio?

A: To simplify the common ratio, you can multiply both the numerator and denominator by a common factor. For example, if you have the common ratio:

$$r = \frac{6x - 10}{8x - 4}$$

You can multiply both the numerator and denominator by 2 to simplify it:

$$r = \frac{(6x - 10)(2)}{(8x - 4)(2)} = \frac{12x - 20}{16x - 8}$$

Q: How do I find the expression for PS in a geometric sequence?

A: To find the expression for PS, you can multiply PR by the common ratio:

$$PS = PR \cdot r = (4x - 2) \cdot \frac{6x - 10}{8x - 4}$$

Q: How do I simplify the expression for PS?

A: To simplify the expression for PS, you can multiply the numerator and denominator by a common factor. For example, if you have the expression:

$$PS = (4x - 2) \cdot \frac{(6x - 10)(4)}{(8x - 4)(4)}$$

You can multiply both the numerator and denominator by 2 to simplify it:

$$PS = \frac{(4x - 2)(6x - 10)(2)}{(8x - 4)(2)} = \frac{(8x - 4)(6x - 10)}{(8x - 4)}$$

Q: Can I cancel out the common factor in the numerator and denominator?

A: Yes, you can cancel out the common factor in the numerator and denominator. For example, if you have the expression:

$$PS = \frac{(8x - 4)(6x - 10)}{(8x - 4)}$$

You can cancel out the common factor (8x - 4) in the numerator and denominator:

$$PS = 6x - 10$$

Conclusion

In this article, we have answered some frequently asked questions related to solving for PS in a geometric sequence. We hope this article has provided you with a better understanding of how to find the expression that represents the segment PS in a geometric sequence.

Frequently Asked Questions

• What is a geometric sequence?
• How do I find the common ratio in a geometric sequence?
• How do I simplify the common ratio?
• How do I find the expression for PS in a geometric sequence?
• How do I simplify the expression for PS?
• Can I cancel out the common factor in the numerator and denominator?

Answer Key

• A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
• To find the common ratio, you can divide any two adjacent terms in the sequence.
• To simplify the common ratio, you can multiply both the numerator and denominator by a common factor.
• To find the expression for PS, you can multiply PR by the common ratio.
• To simplify the expression for PS, you can multiply the numerator and denominator by a common factor.
• Yes, you can cancel out the common factor in the numerator and denominator.