Arithmetic Sequence Generator
Generate an arithmetic sequence online using its first term and common difference. Calculate individual terms, the nth term, and the sum of the first n terms. Explore increasing, decreasing, and constant sequences.
Generate an arithmetic sequence
Enter the starting value, common difference, and number of terms.
What is an arithmetic sequence?
An arithmetic sequence is a list of numbers in which the difference between each pair of consecutive terms is constant. This value is called the common difference and is represented by d.
For example, 3, 8, 13, 18, 23, ... is an arithmetic sequence because 5 is added each time. The first term is 3 and the common difference is 5.
Arithmetic sequence formulas
1. Find the nth term
The formula calculates any term directly. For example, if a₁ = 3 and d = 5, the eighth term is 3 + (8 − 1) × 5 = 38.
2. Sum of the first n terms
When the last term is not already known, use the equivalent formula below.
3. Common difference
Subtract any term from the next term to find the common difference. For an arithmetic sequence, this difference remains the same throughout.
Examples of arithmetic sequences
Increasing sequence
The common difference is 5.
Decreasing sequence
The common difference is −3.
Constant sequence
The common difference is 0.
Decimal sequence
The common difference is 0.5.
Frequently asked questions
What is an arithmetic sequence?
An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant. This fixed value is called the common difference.
What is the formula for the nth term?
The nth term is a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the position of the term.
How do you calculate the sum of an arithmetic sequence?
The sum of the first n terms is S_n = n/2 times (2a_1 + (n - 1)d). Equivalently, S_n = n(a_1 + a_n)/2.
Can the common difference be negative?
Yes. A negative common difference creates a sequence that decreases by the same amount at each step.
What happens when the common difference is zero?
Every term equals the first term. The sum of n terms is n times the first term.
How many terms can I generate?
This calculator generates between 1 and 200 terms per calculation.