/*! 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 139 What is the common ratio in a ge... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 139

What is the common ratio in a geometric sequence?

Short Answer

Expert verified
The common ratio in a geometric sequence is a fixed, non-zero real number that each term is multiplied by to produce the subsequent term in the sequence.

Step by step solution

01

Understand the definition of the common ratio

In a geometric sequence, any term divided by its preceding term gives the common ratio. This means, if the sequence is denoted as \( a, ar, ar^2, ar^3, ar^4, \ldots \), \( r \) is the common ratio.
02

Interpret the common ratio

The common ratio is the factor that multiplies each term to get the next term in the geometric sequence. It is constant for a particular geometric sequence and can be any real number except zero. The value of the common ratio governs the type of the geometric sequence, i.e., increasing, decreasing, alternating etc.

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 sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,-18,-30, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=5000, r=1\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=1000, r=-\frac{1}{2}\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the first term of an arithmetic sequence is 5 and the third term is \(-3\), then the fourth term is \(-7\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=3, r=-2\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.