Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

Q: The first five terms of the sequence  are: 5,
A:
Q: 4. What is the fourth term in the sequence defined as: a1 126 and an 3(an-1) - 5 %3D %3D
A: A sequence is a function which domain being the set of natural numbers and the range being the set…
Q: What are the initial term and a recursive formula for this sequence: 4, 7, 10, 13, ......
A: The given sequence is 4,7,10,13,... the common difference is 7-4=3,10-7=3,... therefore, the common…
Q: Which term of the arithmetic sequence 7,12,17,... is 352?
A: an=a+(n-1)d
Q: last?dep=23200069 Find the number of terms in the finite arithmetic sequence. -3,0, 3, .., 84
A:
Q: Find the sum of the first 14 terms of the geometric sequence: , 3, -6, 12, ...
A: Given geometric sequence is,
Q: Find the 4 term of the geometric sequence 9, 54, 324, ... Answer:
A: Given : 9 , 54 , 324
Q: 1) Write the next four terms of the sequence: {42, 35, 28, 21, ...}. Express the nth term of the…
A: we have to slove the above question and find next four terms of the sequence
Q: Compute the missing terms in the arithmetic sequence. -38, 562, ...
A:
bartleby

Concept explainers

Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
Topic Video
Question
**Question 11: Write the formula for the nth term of the following sequence: 3, -9, 27, -81, 243, ...** The sequence provided is an alternating geometric sequence. To derive the formula for the nth term, observe the pattern in the sequence. The first term is 3, and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the nth term \(a_n\) of the sequence can be expressed using the formula: \[ a_n = 3 \times (-3)^{n-1} \] This formula will allow you to find any term in the sequence by substituting the position of the term (n) into the formula. For example: - To find the first term (\(a_1\)): \[ a_1 = 3 \times (-3)^{1-1} = 3 \times 1 = 3 \] - To find the second term (\(a_2\)): \[ a_2 = 3 \times (-3)^{2-1} = 3 \times (-3) = -9 \] By examining the common ratio and the signs of the terms, it can be confirmed that the sequence will alternate in sign and increase in magnitude as specified by the formula.
expand button
Transcribed Image Text:**Question 11: Write the formula for the nth term of the following sequence: 3, -9, 27, -81, 243, ...** The sequence provided is an alternating geometric sequence. To derive the formula for the nth term, observe the pattern in the sequence. The first term is 3, and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the nth term \(a_n\) of the sequence can be expressed using the formula: \[ a_n = 3 \times (-3)^{n-1} \] This formula will allow you to find any term in the sequence by substituting the position of the term (n) into the formula. For example: - To find the first term (\(a_1\)): \[ a_1 = 3 \times (-3)^{1-1} = 3 \times 1 = 3 \] - To find the second term (\(a_2\)): \[ a_2 = 3 \times (-3)^{2-1} = 3 \times (-3) = -9 \] By examining the common ratio and the signs of the terms, it can be confirmed that the sequence will alternate in sign and increase in magnitude as specified by the formula.
Expert Solution
Check Mark
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
bartleby
This is a popular solution
See solutionCheck out a sample Q&A here
Step 1
VIEW
Step 2
VIEW
bartleby

Trending nowThis is a popular solution!

bartleby

Step by stepSolved in 2 steps with 2 images

See solution
Check out a sample Q&A here
Blurred answer
Knowledge Booster
Background pattern image
Calculus
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.
Similar questions
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
SEE MORE TEXTBOOKS