Thank you for visiting Given the list of consecutive values write an expression to represent the sequence The sequence values are tex 125 25 5 1 tex 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 solve the problem and determine which expression represents the given sequence [tex]\(-125, -25, -5, -1\)[/tex], let's identify the pattern in this sequence.
1. Identify the Type of Sequence:
- We can notice that each number is multiplied by the same factor to get the next number. This suggests it's a geometric sequence.
2. Find the Common Ratio:
- Take the second term [tex]\(-25\)[/tex] and divide it by the first term [tex]\(-125\)[/tex]:
[tex]\[
\text{common ratio} = \frac{-25}{-125} = 0.2
\][/tex]
- To verify, multiply [tex]\(-125\)[/tex] by [tex]\(0.2\)[/tex] to see if it gives the next term:
- [tex]\(-125 \times 0.2 = -25\)[/tex]
- [tex]\(-25 \times 0.2 = -5\)[/tex]
- [tex]\(-5 \times 0.2 = -1\)[/tex]
- The common ratio is indeed [tex]\(0.2\)[/tex].
3. Write the General Formula for the Geometric Sequence:
- The general form for a geometric sequence is [tex]\(a \cdot r^n\)[/tex], where [tex]\(a\)[/tex] is the first term and [tex]\(r\)[/tex] is the common ratio.
- Here, the first term [tex]\(a = -125\)[/tex] and the common ratio [tex]\(r = 0.2\)[/tex].
- Therefore, the expression for the sequence is:
[tex]\[
-125 \cdot (0.2)^n
\][/tex]
4. Match the Expression with the Given Options:
- The expression we derived [tex]\(-125 \cdot (0.2)^n\)[/tex] matches the option:
[tex]\[
-125 \cdot 0.20^n
\][/tex]
In conclusion, the correct choice that represents the sequence [tex]\(-125, -25, -5, -1\)[/tex] is [tex]\(-125 \cdot 0.20^n\)[/tex].
1. Identify the Type of Sequence:
- We can notice that each number is multiplied by the same factor to get the next number. This suggests it's a geometric sequence.
2. Find the Common Ratio:
- Take the second term [tex]\(-25\)[/tex] and divide it by the first term [tex]\(-125\)[/tex]:
[tex]\[
\text{common ratio} = \frac{-25}{-125} = 0.2
\][/tex]
- To verify, multiply [tex]\(-125\)[/tex] by [tex]\(0.2\)[/tex] to see if it gives the next term:
- [tex]\(-125 \times 0.2 = -25\)[/tex]
- [tex]\(-25 \times 0.2 = -5\)[/tex]
- [tex]\(-5 \times 0.2 = -1\)[/tex]
- The common ratio is indeed [tex]\(0.2\)[/tex].
3. Write the General Formula for the Geometric Sequence:
- The general form for a geometric sequence is [tex]\(a \cdot r^n\)[/tex], where [tex]\(a\)[/tex] is the first term and [tex]\(r\)[/tex] is the common ratio.
- Here, the first term [tex]\(a = -125\)[/tex] and the common ratio [tex]\(r = 0.2\)[/tex].
- Therefore, the expression for the sequence is:
[tex]\[
-125 \cdot (0.2)^n
\][/tex]
4. Match the Expression with the Given Options:
- The expression we derived [tex]\(-125 \cdot (0.2)^n\)[/tex] matches the option:
[tex]\[
-125 \cdot 0.20^n
\][/tex]
In conclusion, the correct choice that represents the sequence [tex]\(-125, -25, -5, -1\)[/tex] is [tex]\(-125 \cdot 0.20^n\)[/tex].
Thank you for reading the article Given the list of consecutive values write an expression to represent the sequence The sequence values are tex 125 25 5 1 tex 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!
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Rewritten by : Jeany
