Arithmetic Sequence Calculator
Enter the first term and the common difference of an arithmetic sequence to find any term and the running total up to that term.
Arithmetic Sequence Calculator
Finds the nth term and the sum of the first n terms of an arithmetic sequence.
An arithmetic sequence increases (or decreases) by a constant amount between terms, and this calculator uses the standard closed-form formulas aₙ = a₁ + (n-1)d and Sₙ = n/2 × (2a₁ + (n-1)d) to find any term and the running sum without you having to add terms one by one. It's a staple of algebra courses but also shows up in finance (level payment schedules), scheduling, and anywhere a quantity changes by a fixed step each period.
Example
- With the default values shown above, this calculator returns: nth Term ≈ 48; Sum of First n Terms ≈ 255.
Frequently Asked Questions
What is an arithmetic sequence?
A sequence where each term is found by adding the same fixed amount (the common difference) to the previous term, e.g. 3, 8, 13, 18…
How is the sum formula derived?
It pairs the first and last term, averages them, and multiplies by the number of terms: n/2 × (2a₁ + (n-1)d), which is algebraically equivalent to n × (first term + last term) / 2.
Sources
- Standard formula, publicly documented method