Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Topic Video
Question
![**Writing a Recursive Formula for a Sequence**
To find the recursive formula for the sequence:
\[
\{-9, -27, -81, -243, -729, \ldots\}
\]
---
### Recursive Formula Components
1. **Initial Term:**
- \( a_1 = \)
- The first term of the sequence is \(-9\).
2. **Recursive Step:**
- \( a_n = \)
- Identify the pattern or rule that defines each subsequent term after the initial term.
### Pattern Analysis
- Observe the sequence: each term is multiplied by the same factor to obtain the next term.
- \( \frac{-27}{-9} = 3 \)
- \( \frac{-81}{-27} = 3 \)
- \( \frac{-243}{-81} = 3 \)
- \( \frac{-729}{-243} = 3 \)
- This is a geometric sequence where each term is obtained by multiplying the previous term by \(-3\).
### Recursive Formula
- **Initial Term:**
\[
a_1 = -9
\]
- **Recursive Rule:**
\[
a_n = -3 \times a_{n-1} \quad \text{for } n \geq 2
\]
This setup allows calculation of any term in the sequence using the previous term.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe17ee3d9-6ebe-435a-ba9d-3c68c44204c7%2Ffac4b2ce-cbc6-4c2b-a828-a2163fd82d99%2F99jeg66_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Writing a Recursive Formula for a Sequence**
To find the recursive formula for the sequence:
\[
\{-9, -27, -81, -243, -729, \ldots\}
\]
---
### Recursive Formula Components
1. **Initial Term:**
- \( a_1 = \)
- The first term of the sequence is \(-9\).
2. **Recursive Step:**
- \( a_n = \)
- Identify the pattern or rule that defines each subsequent term after the initial term.
### Pattern Analysis
- Observe the sequence: each term is multiplied by the same factor to obtain the next term.
- \( \frac{-27}{-9} = 3 \)
- \( \frac{-81}{-27} = 3 \)
- \( \frac{-243}{-81} = 3 \)
- \( \frac{-729}{-243} = 3 \)
- This is a geometric sequence where each term is obtained by multiplying the previous term by \(-3\).
### Recursive Formula
- **Initial Term:**
\[
a_1 = -9
\]
- **Recursive Rule:**
\[
a_n = -3 \times a_{n-1} \quad \text{for } n \geq 2
\]
This setup allows calculation of any term in the sequence using the previous term.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning