---
title: "The Common Difference in an Arithmetic Sequence"
url: https://www.learningloftinstitute.com/glossary/common-difference
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Glossary › The Common Difference in an Arithmetic Sequence"
---
# The Common Difference in an Arithmetic Sequence
> **Answer.** The common difference is the number added to each term of an arithmetic sequence to reach the next one. Find it by subtracting a term from the one after it: in 5, 8, 11, 14 the common difference is 3. A decreasing sequence has a negative common difference.
## Key facts
| | |
| --- | --- |
| Definition | The fixed amount added to each term of an arithmetic sequence to get the next one, found by subtracting any term from the one that follows it. |
| Where students meet it | Grade 8 mathematics, and again in every GCSE and IGCSE question that asks for the nth term of an arithmetic sequence. |
| Also known as | d, in the nth term formula |
## How to find it
Subtract each term from the one that follows it. In 5, 8, 11, 14, 17 the four subtractions all give 3, so the common difference is 3 and the sequence is arithmetic. Every further term is one more addition away.
The word common is doing real work in the name. It is not enough that one pair of terms differs by 3; every adjacent pair has to differ by 3, all the way along.
The value is also the coefficient of n in the nth term rule, which is why teachers ask for it first. A sequence rising in 3s has a rule of the form 3n plus a constant, and the constant is only ever the shift needed to land on the first term.
## Falling sequences have a negative one
In 20, 17, 14, 11 the subtractions give −3 every time, so the common difference is −3, not 3. The minus sign is part of the value, and losing it turns a sequence that falls into one that rises.
Nothing requires a whole number either. In 1, 1.5, 2, 2.5 the common difference is 0.5, and in a sequence going up in quarters it is one quarter. Fractions and decimals behave exactly the same way under subtraction.
Sequences taken from real situations carry units with them. A tank losing 6 litres an hour gives an arithmetic sequence with a common difference of −6 litres, and the minus sign is what records the loss rather than a gain.
## One pair proves nothing
Look at 2, 4, 8, 16. The first two terms differ by 2, and a student who stops there writes down a common difference of 2 and an nth term of 2n. The next pair differs by 4 and the pair after that by 8. The sequence is not arithmetic at all — it is geometric, with each term doubled.
So finding the common difference is a test rather than a single subtraction. Work out every difference the given terms allow, and only call the answer a common difference once they all agree.
## Questions
### Can the common difference be a fraction or a negative number?
Both. In 1, 1.5, 2, 2.5 it is 0.5, and in 20, 17, 14, 11 it is −3. The only thing that matters is that the same amount is added each time; adding a negative amount is what makes a sequence decrease, and it is still called the common difference.
### What is the difference between a common difference and a common ratio?
A common difference is added, a common ratio is multiplied. Arithmetic sequences step up or down by a fixed amount, so you find the pattern by subtracting. Geometric sequences scale by a fixed factor, so you find the pattern by dividing. If subtraction gives no consistent answer, try division before deciding there is no rule.
### How do I find the common difference from two terms that are not next to each other?
Count the steps between them and divide. If the 3rd term is 10 and the 7th term is 26, there are four steps from one to the other and the terms have risen by 16, so the common difference is 16 ÷ 4 = 4. The same method works when the gap is negative.
### Is a sequence with a common difference of zero still arithmetic?
Yes. In 7, 7, 7, 7 the same amount — nothing — is added each time, so it satisfies the definition with a common difference of 0. It is a legitimate arithmetic sequence, just a constant one, and its nth term rule is simply 7.
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