/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 Write the first four terms of ea... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 10

Write the first four terms of each sequence whose general term is given. $$a_{n}=\frac{3 n}{n+5}$$

Short Answer

Expert verified
The first four terms of the sequence are \(a_{1} = \frac{1}{2}\), \(a_{2} = \frac{6}{7}\), \(a_{3} = \frac{9}{8}\), and \(a_{4} = \frac{4}{3}\).

Step by step solution

01

Determine the First Term

By substituting \(n = 1\) into \(a_{n}=\frac{3n}{n+5}\), we get the first term as \(a_{1} = \frac{3(1)}{1+5} = \frac{1}{2}\).
02

Determine the Second Term

Substitute \(n = 2\) into the equation \(a_{n}=\frac{3n}{n+5}\). That gives us the second term: \(a_{2} = \frac{3(2)}{2+5} = \frac{6}{7}\).
03

Determine the Third Term

Substitute \(n = 3\) into the equation \(a_{n}=\frac{3n}{n+5}\). That gives us the third term: \(a_{3} = \frac{3(3)}{3+5} = \frac{9}{8}\).
04

Determine the Fourth Term

Finally, substitute \(n = 4\) into \(a_{n}=\frac{3n}{n+5}\). That gives us the fourth term: \(a_{4} = \frac{3(4)}{4+5} = \frac{4}{3}\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Factor: \(27 x^{3}-8\) (Section 6.4, Example 8)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. An arithmetic sequence is a linear function whose domain is the set of natural numbers

Use the formula for the general term (the nth term) of a geometric sequence to solve. A professional baseball player signs a contract with a beginning salary of \(\$ 3,000,000\) for the first year and an annual increase of \(4 \%\) per year beginning in the second year. That is, beginning in year \(2,\) the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\sum_{i=1}^{2} a_{i} b_{i}=\sum_{i=1}^{2} a_{i} \sum_{i=1}^{2} b_{i}$$

Use the formula for the value of an annuity to solve Exercises. Round answers to the nearest dollar. To save money for a sabbatical to earn a master's degree, you deposit \(\$ 2000\) at the end of each year in an annuity that pays \(7.5 \%\) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.