Arithmetic Sequence Calculator
Find a term and partial sum of an arithmetic sequence
nth term
How we calculated it
About the Arithmetic Sequence Calculator
An arithmetic sequence changes by the same fixed amount from one term to the next. That constant difference makes it possible to jump directly to a later term without listing every value in between.
The same structure also gives a compact formula for the sum of a finite number of terms.
How to Use the Arithmetic Sequence Calculator
- Enter the first term.
- Enter the common difference.
- Enter the term number or number of terms you want to evaluate.
- Calculate the requested term or sequence sum.
How the Calculation Works
The nth term is a_n = a₁ + (n−1)d, where a₁ is the first term and d is the common difference.
The sum of the first n terms is S_n = n/2 × [2a₁ + (n−1)d], equivalent to n(a₁+a_n)/2.
Worked example
Arithmetic Sequence Calculator Worked Example
Sequence 5, 8, 11, 14, …
The common difference is 3. The 10th term is 5+(10−1)×3 = 5+27 = 32. The sum of the first 10 terms is 10×(5+32)÷2 = 185.
Result guide
Understanding Your Arithmetic Sequence Calculator Result
A positive common difference makes the sequence rise linearly; a negative difference makes it fall. A difference of zero produces a constant sequence. Because the change is constant, plotting term number against term value produces a straight-line pattern, which is why arithmetic sequences are closely related to linear functions.
Before you rely on the answer
Assumptions and Limitations
- Each consecutive term changes by the same common difference.
- Term number n is a positive integer.
- Finite-sum formulas use the specified first n terms.
Practical tip
Using This Result in Practice
Check the first few terms using the formula before jumping to a distant term. It is an easy way to catch a sign error in the common difference. If the first listed term is not term 1, adjust the index carefully before using the standard nth-term formula.
Related calculations
Useful Calculations to Continue With
If each term is multiplied by the same factor instead of adding the same difference, use the Geometric Sequence Calculator.
Arithmetic sequences are closely related to linear relationships; use the Linear Equation Calculator when the same change is written as an equation.
Common questions
Arithmetic Sequence Calculator FAQ
What is the common difference?
It is the constant amount added to one term to obtain the next term.
How do I find the nth arithmetic term?
Use a_n=a₁+(n−1)d.
Can an arithmetic sequence decrease?
Yes. A negative common difference makes each successive term smaller.