Common Difference - Varsity Tutors

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Common Difference

Study Guide

Key Definition

The constant difference between consecutive terms of an arithmetic sequence is called the common difference. For example, in the sequence 9, 7, 5, 3, ... the common difference is $-2$.

Important Notes

  • The common difference can be calculated by subtracting any term from the term that follows it.
  • In an arithmetic sequence, the common difference is constant.
  • The common difference can be positive, negative or zero.

Mathematical Notation

Let $d$ denote the common difference. It can be calculated as $d = a_{n+1} - a_n$.Remember to use proper notation when solving problems

Why It Works

An arithmetic sequence has a constant difference because it increases or decreases by a regular interval. This interval is what we call the common difference.

Remember

The common difference is the key to understanding the pattern of an arithmetic sequence. It helps you predict future terms and understand the structure of the sequence.

Quick Reference

Common Difference:$d = a_{n+1} - a_n$

Understanding Common Difference

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Video explanation of this concept

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Beginner Explanation

In an arithmetic sequence like 2, 4, 6, 8, ... the common difference is $2$ because each term increases by $2$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the common difference in the arithmetic sequence 3, 6, 9, 12, ...?

A$2$B$3$C$4$D$6$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Music Playlist Scenario

Imagine you are creating a playlist where each song is $3$ minutes longer than the previous one. If the first three songs are $2$, $5$, and $8$ minutes long, how long will the fourth song be?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Which of the following is an arithmetic sequence?

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

Recap

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Review key concepts and takeaways

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