Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 30, -120, 480, ... Sum of a finite geometric series: a₁ - arn Sn = 1-r
Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 30, -120, 480, ... Sum of a finite geometric series: a₁ - arn Sn = 1-r
Chapter12: Sequences, Series And Binomial Theorem
Section: Chapter Questions
Problem 328PT: Find the first term and common difference of an arithmetic sequence whose ninth term is -1 and the...
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![### Finding the Sum of a Geometric Sequence
**Problem Statement:**
Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary.
\[30, \, -120, \, 480, \, \ldots\]
**Sum of a Finite Geometric Series:**
To find the sum of a finite geometric series, we use the formula:
\[
S_n = \frac{a_1 - a_1 r^n}{1 - r}
\]
where:
- \( S_n \) is the sum of the first \( n \) terms.
- \( a_1 \) is the first term of the sequence.
- \( r \) is the common ratio.
- \( n \) is the number of terms.
**Explanation of Terms:**
- **First Term (\( a_1 \))**: This is the initial term of the sequence. For the given sequence, \( a_1 = 30 \).
- **Common Ratio (\( r \))**: This can be found by dividing the second term by the first term. For the sequence, the common ratio \( r \) is \(\frac{-120}{30} = -4 \).
- **Number of Terms (\( n \))**: For this problem, \( n = 9 \).
By plugging the values into the formula, we can calculate the sum of the first 9 terms of the given geometric sequence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f36c12-bb42-44cf-b4d7-4a7cf773a344%2Ff19fd8cf-aa93-4cdb-a1a8-62d9df7d1dd9%2F8paqoo7_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding the Sum of a Geometric Sequence
**Problem Statement:**
Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary.
\[30, \, -120, \, 480, \, \ldots\]
**Sum of a Finite Geometric Series:**
To find the sum of a finite geometric series, we use the formula:
\[
S_n = \frac{a_1 - a_1 r^n}{1 - r}
\]
where:
- \( S_n \) is the sum of the first \( n \) terms.
- \( a_1 \) is the first term of the sequence.
- \( r \) is the common ratio.
- \( n \) is the number of terms.
**Explanation of Terms:**
- **First Term (\( a_1 \))**: This is the initial term of the sequence. For the given sequence, \( a_1 = 30 \).
- **Common Ratio (\( r \))**: This can be found by dividing the second term by the first term. For the sequence, the common ratio \( r \) is \(\frac{-120}{30} = -4 \).
- **Number of Terms (\( n \))**: For this problem, \( n = 9 \).
By plugging the values into the formula, we can calculate the sum of the first 9 terms of the given geometric sequence.
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