Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To find the 8th term of a geometric sequence, we need a few key pieces of information:
1. The first term of the sequence (\(a\)).
2. The common ratio (\(r\)).
3. The position of the term we want to find (\(n\)).
Given:
- The first term (\(a\)) is 9.
- The common ratio (\(r\)) is -3.
- The term we are looking for is the 8th term (\(n = 8\)).
The formula for the \(n\)-th term of a geometric sequence is:
[tex]\[ a_n = a \cdot r^{(n-1)} \][/tex]
Let's plug the given values into the formula:
[tex]\[ a_8 = 9 \cdot (-3)^{(8-1)} \][/tex]
[tex]\[ a_8 = 9 \cdot (-3)^7 \][/tex]
Now we need to evaluate \((-3)^7\):
[tex]\[-3^7 = -3 \times -3 \times -3 \times -3 \times -3 \times -3 \times -3\][/tex]
Since the exponent is an odd number, the result of raising a negative number to an odd power is negative:
[tex]\[ (-3)^7 = -2187 \][/tex]
Now we multiply this result by the first term:
[tex]\[ a_8 = 9 \cdot (-2187) \][/tex]
[tex]\[ a_8 = -19683 \][/tex]
So, the 8th term of the geometric sequence is \(-19683\).
Among the given options, the correct answer is:
- [tex]\(-19,683\)[/tex].
1. The first term of the sequence (\(a\)).
2. The common ratio (\(r\)).
3. The position of the term we want to find (\(n\)).
Given:
- The first term (\(a\)) is 9.
- The common ratio (\(r\)) is -3.
- The term we are looking for is the 8th term (\(n = 8\)).
The formula for the \(n\)-th term of a geometric sequence is:
[tex]\[ a_n = a \cdot r^{(n-1)} \][/tex]
Let's plug the given values into the formula:
[tex]\[ a_8 = 9 \cdot (-3)^{(8-1)} \][/tex]
[tex]\[ a_8 = 9 \cdot (-3)^7 \][/tex]
Now we need to evaluate \((-3)^7\):
[tex]\[-3^7 = -3 \times -3 \times -3 \times -3 \times -3 \times -3 \times -3\][/tex]
Since the exponent is an odd number, the result of raising a negative number to an odd power is negative:
[tex]\[ (-3)^7 = -2187 \][/tex]
Now we multiply this result by the first term:
[tex]\[ a_8 = 9 \cdot (-2187) \][/tex]
[tex]\[ a_8 = -19683 \][/tex]
So, the 8th term of the geometric sequence is \(-19683\).
Among the given options, the correct answer is:
- [tex]\(-19,683\)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.