Arithmetic Sequence

A sequence where each term differs from the previous by a constant amount (common difference).

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A sequence where each term differs from the previous by a constant amount (common difference).

An arithmetic sequence (also called arithmetic progression) is a sequence of numbers where the difference between consecutive terms is constant. This constant is called the 'common difference'. Arithmetic sequences are among the most fundamental patterns in mathematics and appear frequently in real-world situations like counting, scheduling, and linear growth.

aₙ = a₁ + (n-1)d, where d is the common difference

2, 5, 8, 11, 14... (common difference = +3)
20, 17, 14, 11, 8... (common difference = -3)
1, 1, 1, 1, 1... (common difference = 0)

How to recognize it

Calculate the difference between consecutive terms
If all differences are the same, it's arithmetic
The pattern is 'add (or subtract) the same number each time'

Common mistakes

Confusing with geometric sequences (multiply vs add)
Miscounting when the common difference is negative
Forgetting that constant sequences (d=0) are also arithmetic

Step-by-step walkthrough

Find the next term: 2, 5, 8, 11, ?

Calculate differences: 5-2=3, 8-5=3, 11-8=3
All differences are the same: common difference = 3
This is arithmetic. Add 3 to the last term
The next term is 14

Answer: 14

Practice guidance

Number Sequences