Chapter 12: Q 29. (page 809)

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
role="math" localid="1646738144824" $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, . . .$

Short Answer

Expert verified

The nth term of the sequence is $a_{n} = \frac{n}{n + 1}$

Step by step solution

Step 1. Write the given information

The given sequence is $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, . . .$

Step 2. Determine the pattern of the sequence and write down the nth term.

$a_{1} = \frac{1}{2}, a_{2} = \frac{2}{3}, a_{3} = \frac{3}{4}$

The pattern of the sequence is:

$a_{1} = \frac{1}{2} = \frac{1}{1 + 1} a_{2} = \frac{2}{3} = \frac{2}{2 + 1} a_{3} = \frac{3}{4} = \frac{3}{3 + 1} a_{n} = \frac{n}{n + 1}$

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 Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
role="math" localid="1646738144824" $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, . . .$

Short Answer

Step by step solution

Step 1. Write the given information

Step 2. Determine the pattern of the sequence and write down the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Statistics

Decision Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.role="math" localid="1646738144824" 12,23,34,45,...

Short Answer

Step by step solution

Step 1. Write the given information

Step 2. Determine the pattern of the sequence and write down the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Statistics

Decision Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
role="math" localid="1646738144824" $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, . . .$