/*! 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 1 What is an arithmetic sequence? ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 1

What is an arithmetic sequence? Give an example.

Short Answer

Expert verified
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant, called the common difference (denoted as \(d\)). The general form is \(a_n = a_1 + (n - 1)d\). An example of an arithmetic sequence is \[ 3, 7, 11, 15, 19, \dots \] with a common difference of 4.

Step by step solution

01

Define Arithmetic Sequence

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always constant. This constant difference is called the common difference and is usually denoted by \(d\).
02

General Form

The general form of an arithmetic sequence can be written as: \(a_n = a_1 + (n - 1)d\), where \(a_n\) is the \(n\)-th term, \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference.
03

Example of Arithmetic Sequence

We will provide an example of an arithmetic sequence. Consider the sequence: \[ 3, 7, 11, 15, 19, \dots \]
04

Verify the Common Difference

To confirm that this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant: - Difference between the second term (7) and the first term (3) is \(7 - 3 = 4\). - Difference between the third term (11) and the second term (7) is \(11 - 7 = 4\). - Difference between the fourth term (15) and the third term (11) is \(15 - 11 = 4\). - Difference between the fifth term (19) and the fourth term (15) is \(19 - 15 = 4\). Since the difference between consecutive terms is constant and equal to 4, this sequence is an arithmetic sequence with a common difference of 4.

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

Evaluate each binomial coefficient. $$\left(\begin{array}{l}7 \\\3\end{array}\right)$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$4,-12,36,-108, \dots$$

Find the indicated term of each binomial expansion. $$\left(2 y^{2}+z\right)^{10} ; \text { eighth term }$$

A ball is dropped from a height of 16 ft. Each time the ball bounces it rebounds to \(\frac{3}{4}\) of its previous height. a) Find the height the ball reaches after the fourth bounce. b) Find the total vertical distance the ball has traveled when it comes to rest.

Use Pascal鈥檚 Triangle to expand each binomial. $$(x+5)^{4}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Pure Maths

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.