Chapter 12: Q. 13 (page 816)

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{s_{n}\} = \{\ln 3^{n}\}$

Short Answer

Expert verified

The solution is $d = \ln 3$ ; first four terms $= \ln 3, \ln 9, \ln 27, \ln 81$ .

Step by step solution

Step 1. Given information

$\{s_{n}\} = \{\ln 3^{n}\}$

Step 2. Calculation

The first term is $s_{1} = \ln 3^{1} = \ln 3$

The $n$ th term and the $(n - 1)$ st term of the sequence are-

$s_{n} = \ln 3^{n}$ and localid="1649248765654" $s_{n - 1} = \ln 3^{n - 1}$

The common difference is -

$d = s_{n} - s_{n - 1} = \ln 3^{n} - \ln 3^{n - 1} = (n \ln 3) - (n \ln 3 - \ln 3) = \ln 3$

Since the difference of any two successive terms is the constant $\ln 3$ , the sequence $\{s_{n}\}$ is arithmetic.

The first four terms are localid="1649312212704" $\ln 3, \ln 9, \ln 27, \ln 81$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{s_{n}\} = \{\ln 3^{n}\}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Geometry

Probability and Statistics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.sn=ln3n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Geometry

Probability and Statistics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.
$\{s_{n}\} = \{\ln 3^{n}\}$