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What is the difference between two terms in an arithmetic sequence?

Published in Arithmetic Sequences 2 mins read

The difference between any two consecutive terms in an arithmetic sequence is called the common difference.

Understanding Arithmetic Sequences and the Common Difference

An arithmetic sequence is defined by a constant difference between successive terms. This constant difference is crucial for understanding the sequence and is known as the common difference.

  • Definition: An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is constant.
  • Common Difference: According to the reference, the common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.

Examples of Common Difference

Here are a few examples to illustrate the common difference:

  • Sequence: 2, 4, 6, 8, 10...
    • Common Difference: 2 (Each term is 2 more than the previous term.)
  • Sequence: 1, 5, 9, 13, 17...
    • Common Difference: 4 (Each term is 4 more than the previous term.)
  • Sequence: 10, 7, 4, 1, -2...
    • Common Difference: -3 (Each term is -3 more than the previous term.)

How to Find the Common Difference

To find the common difference, simply subtract any term from the term that follows it.

  • Formula: d = an+1 - an, where 'd' is the common difference, an+1 is the (n+1)th term, and an is the nth term.

Importance of the Common Difference

The common difference is fundamental in working with arithmetic sequences:

  • It allows you to predict future terms in the sequence.
  • It is used in formulas for calculating the sum of arithmetic series.