1Cademy - Common Difference of an Arithmetic Sequence

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Arithmetic Sequence

Definition

Common Difference of an Arithmetic Sequence

The common difference of an arithmetic sequence, denoted by $d$ , is the constant value obtained when any term is subtracted from the term that directly follows it. Formally, $d = a_n - a_{n-1}$ for every integer $n \geq 2$ . The common difference can be positive, negative, or zero. When $d > 0$ the terms increase (e.g., $5, 9, 13, 17, \dots$ has $d = 4$ ); when $d < 0$ the terms decrease (e.g., $10, 3, -4, -11, \dots$ has $d = -7$ ); and when $d = 0$ every term is identical. To verify that a sequence is arithmetic, compute the difference between each pair of consecutive terms: if all differences equal the same value, that value is $d$ .