Thank you for visiting Given the sequence tex 125 25 5 ldots tex Which of the following rules tex j n tex uses the geometric sequence formula A tex. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine the rule for the given sequence [tex]\(125, 25, 5, \ldots\)[/tex], we need to verify if it follows a geometric progression and find the formula that represents it.
### Step-by-Step Solution:
1. Identify the terms:
You have a sequence starting with the numbers 125, 25, and 5.
2. Calculate the common ratio:
In a geometric sequence, each term after the first is obtained by multiplying the previous term by a constant called the common ratio ([tex]\(r\)[/tex]).
- Calculate the ratio between the second term and the first term:
[tex]\[
r = \frac{25}{125} = \frac{1}{5}
\][/tex]
- Calculate the ratio between the third term and the second term to confirm it is consistent:
[tex]\[
\frac{5}{25} = \frac{1}{5}
\][/tex]
Since both calculations give the same result, [tex]\(\frac{1}{5}\)[/tex], we confirm the sequence is geometric with a common ratio of [tex]\(\frac{1}{5}\)[/tex].
3. Write the general formula:
The formula for the [tex]\(n\)[/tex]-th term of a geometric sequence is:
[tex]\[
j(n) = a \cdot r^{(n-1)}
\][/tex]
where [tex]\(a\)[/tex] is the first term of the sequence.
- Here, [tex]\(a = 125\)[/tex] and [tex]\(r = \frac{1}{5}\)[/tex].
So, the formula becomes:
[tex]\[
j(n) = 125 \cdot \left(\frac{1}{5}\right)^{n-1}
\][/tex]
4. Choose the correct option:
After determining the formula, we identify it with option A:
[tex]\[
j(n) = 125 \cdot \left(\frac{1}{5}\right)^{n-1}
\][/tex]
Thus, the rule for the sequence is given by option A.
### Step-by-Step Solution:
1. Identify the terms:
You have a sequence starting with the numbers 125, 25, and 5.
2. Calculate the common ratio:
In a geometric sequence, each term after the first is obtained by multiplying the previous term by a constant called the common ratio ([tex]\(r\)[/tex]).
- Calculate the ratio between the second term and the first term:
[tex]\[
r = \frac{25}{125} = \frac{1}{5}
\][/tex]
- Calculate the ratio between the third term and the second term to confirm it is consistent:
[tex]\[
\frac{5}{25} = \frac{1}{5}
\][/tex]
Since both calculations give the same result, [tex]\(\frac{1}{5}\)[/tex], we confirm the sequence is geometric with a common ratio of [tex]\(\frac{1}{5}\)[/tex].
3. Write the general formula:
The formula for the [tex]\(n\)[/tex]-th term of a geometric sequence is:
[tex]\[
j(n) = a \cdot r^{(n-1)}
\][/tex]
where [tex]\(a\)[/tex] is the first term of the sequence.
- Here, [tex]\(a = 125\)[/tex] and [tex]\(r = \frac{1}{5}\)[/tex].
So, the formula becomes:
[tex]\[
j(n) = 125 \cdot \left(\frac{1}{5}\right)^{n-1}
\][/tex]
4. Choose the correct option:
After determining the formula, we identify it with option A:
[tex]\[
j(n) = 125 \cdot \left(\frac{1}{5}\right)^{n-1}
\][/tex]
Thus, the rule for the sequence is given by option A.
Thank you for reading the article Given the sequence tex 125 25 5 ldots tex Which of the following rules tex j n tex uses the geometric sequence formula A tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
