Mathematics · Precalculus
Arithmetic Sequence Calculator
Find the nth term of a sequence with a constant difference.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- From term 1 to term 10 there are 9 jumps.
- Change = 9 × 3 = 27.
- a_10 = 5 + 27 = 32.
Problem → model → reason → result
What problem does this model solve?
Find the nth term of a sequence with a constant difference.
Why does the model apply?
There are n−1 equal jumps from the first term to the nth term, each adding the common difference d.
What assumptions does it make?
The entered values lie in the function's real domain, the stated sequence or function family matches the problem, and angle units are used consistently.
Formula
aₙ = a₁ + (n−1)d
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
With first term 5 and difference 3, term 10 is 5+9×3=32.
Common mistake
Use n−1 differences because the first term occurs before any jump.
When does this model not apply?
A numerical function value does not by itself establish a trend outside the chosen domain, and finite sequences should not be treated automatically as infinite ones.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Arithmetic sequence do?
Find the nth term of a sequence with a constant difference.
How does the Arithmetic sequence work?
The calculator applies aₙ = a₁ + (n−1)d. There are n−1 equal jumps from the first term to the nth term, each adding the common difference d.
What can I learn from the Arithmetic sequence?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.