Common Ratio - Varsity Tutors

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Common Ratio

Study Guide

Key Definition

The constant factor between consecutive terms of a geometric sequence is called the common ratio. It is denoted as $r$.

Important Notes

  • The common ratio can be found by dividing a term in the sequence by the preceding term.
  • The common ratio for the geometric sequence 2 , 4 , 8 , 16 , ... is $\frac{4}{2} = 2$.

Mathematical Notation

$r = \frac{a_n}{a_{n-1}}$ means the common ratio is the quotient of a term and the term preceding it.Remember to use proper notation when solving problems

Why It Works

The common ratio works because it is a constant value that multiplies or divides terms in a geometric sequence.

Remember

The value of the common ratio $r$ determines whether the geometric sequence increases, decreases or remains the same.

Quick Reference

Common Ratio Formula:$r = \frac{a_n}{a_{n-1}}$

Understanding Common Ratio

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

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Beginner Explanation

In a geometric sequence, the common ratio is the constant value by which each term is multiplied to get the next term.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the common ratio in the geometric sequence 3, 6, 12, 24, ...?

A$1$B$2$C$3$D$4$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Concert Tickets Scenario

A band's concert tickets sell out quickly. The number of tickets sold doubles every hour. If the band sold 5 tickets in the first hour, how many tickets would they sell in the 4th hour?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Given the geometric sequence 5, 10, 20, 40, ..., what would be the 7th term?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

If the 3rd term in a geometric sequence is 27 and the 6th term is 729, what is the common ratio?

A$2$B$3$C$4$D$5$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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