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...
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![**Topic: Geometric Sequences**
**Problem:**
The first term and a recursive formula for a geometric sequence are given. Find \(a_6\).
\[
a_1 = 6 \quad , \quad a_n = -4a_{n-1}
\]
**Solution:**
Calculate \(a_6\):
\[
a_6 = ?
\]
Recursive Calculation:
\[
a_2 = (-4)(6) = -24
\]
\[
a_3 = (-4)(-24) = 96
\]
\[
a_4 = (-4)(96) = -384
\]
\[
a_5 = (-4)(-384) = 1536
\]
\[
a_6 = (-4)(1536) = -6144
\]
The calculation results in:
\[
a_6 = -6144
\]
Note: The previous answer was \(-111,9744\), indicating a possible calculation error. Calculating step-by-step is crucial for accuracy in recursive sequences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F431cf26f-8932-45f0-affc-3190a37be4f5%2Fae98d2e8-b684-4b33-a75e-26580be5a55a%2Fj74d8lg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Geometric Sequences**
**Problem:**
The first term and a recursive formula for a geometric sequence are given. Find \(a_6\).
\[
a_1 = 6 \quad , \quad a_n = -4a_{n-1}
\]
**Solution:**
Calculate \(a_6\):
\[
a_6 = ?
\]
Recursive Calculation:
\[
a_2 = (-4)(6) = -24
\]
\[
a_3 = (-4)(-24) = 96
\]
\[
a_4 = (-4)(96) = -384
\]
\[
a_5 = (-4)(-384) = 1536
\]
\[
a_6 = (-4)(1536) = -6144
\]
The calculation results in:
\[
a_6 = -6144
\]
Note: The previous answer was \(-111,9744\), indicating a possible calculation error. Calculating step-by-step is crucial for accuracy in recursive sequences.
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