/*! 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 6 Write the first four terms of ea... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 6

Write the first four terms of each sequence whose general term is given. $$a_{n}=\left(-\frac{1}{3}\right)^{n}$$

Short Answer

Expert verified
The first four terms of the sequence are \(-\frac{1}{3}, \frac{1}{9}, -\frac{1}{27}, \frac{1}{81}\).

Step by step solution

01

- Substituting n = 1

First, substitute \(n = 1\) into \(a_{n}\). The result is \(a_{1} = \left(-\frac{1}{3}\right)^1 = -\frac{1}{3}.\)
02

- Substituting n = 2

Next, substitute \(n = 2\) into \(a_{n}\). The result is \(a_{2} = \left(-\frac{1}{3}\right)^2 = \frac{1}{9}.\)
03

- Substituting n = 3

Now, substitute \(n = 3\) into \(a_{n}\). The result is \(a_{3} = \left(-\frac{1}{3}\right)^3 = -\frac{1}{27}.\)
04

- Substituting n = 4

Lastly, substitute \(n = 4\) into \(a_{n}\). The result is \(a_{4} = \left(-\frac{1}{3}\right)^4 = \frac{1}{81}.\)

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.

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

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

Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. $$1 \cdot 3,2 \cdot 4,3 \cdot 5,4 \cdot 6, \dots$$

Explain how to find the sum of the first \(n\) terms of a geometric sequence without having to add up all the terms.

Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. $$\begin{aligned}&f_{1}(x)=(x+1)^{4} & f_{2}(x)=x^{4}\\\&f_{3}(x)=x^{4}+4 x^{3} & f_{4}(x)=x^{4}+4 x^{3}+6 x^{2}\\\&f_{5}(x)=x^{4}+4 x^{3}+6 x^{2}+4 x\\\&f_{6}(x)=x^{4}+4 x^{3}+6 x^{2}+4 x+1\end{aligned}$$ Use a \([-5,5,1]\) by \([-30,30,10]\) viewing rectangle.

Rationalize the denominator: \(\frac{6}{\sqrt{3}-\sqrt{5}}\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.