Number Sequence Calculator · Practical guide
How to Find the Nth Term of an Arithmetic Sequence
One formula finds any term instantly: aₙ = a₁ + (n − 1)d. Here is how to use it.
At a glance
The Nth Term Formula
For an arithmetic sequence — one that changes by a constant difference — the nth term is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. You never need to list every term; one multiplication and one addition get you straight to the answer.
Interactive tool
Number Sequence Calculator
Enter your own values, then compare the result with the examples below.
Arithmetic Sequence Result
First 10 terms:
Geometric Sequence Result
First 10 terms:
Worked Example
Take the sequence 3, 7, 11, 15, … The first term is a₁ = 3 and the common difference is d = 4. To find the 15th term: a₁₅ = 3 + (15 − 1) × 4 = 3 + 56 = 59.
Finding the Sum Too
The sum of the first n terms uses Sₙ = n/2 × (2a₁ + (n − 1)d). For the same sequence: S₁₅ = 15/2 × (6 + 56) = 7.5 × 62 = 465. The calculator above returns both the nth term and the sum of the first n terms, plus a list of the first 10 terms so you can sanity-check the pattern.
Common Mistakes to Avoid
- Using n instead of (n − 1): the first term itself needs zero jumps, so the multiplier is always one less than the term number
- Missing a negative difference: in 20, 17, 14, … the difference is d = −3, so the 10th term is 20 + 9 × (−3) = −7
- Applying the arithmetic formula to a geometric sequence, where terms multiply instead of add — check that the gaps between terms are constant first
Frequently Asked Questions
How do I find the common difference?
Subtract any term from the term that follows it. If 7 − 3 = 4 and 11 − 7 = 4, the common difference d is 4. The subtraction must give the same value everywhere for the sequence to be arithmetic.
Can the nth term formula handle decimals or fractions?
Yes. The formula aₙ = a₁ + (n − 1)d works with any real numbers — for example a₁ = 0.5 and d = 0.25 gives a₅ = 0.5 + 4 × 0.25 = 1.5.
How do I find which term number a given value is?
Rearrange the formula: n = (aₙ − a₁)/d + 1. For the sequence 3, 7, 11, …, the value 39 gives n = (39 − 3)/4 + 1 = 10, so 39 is the 10th term.
What is the difference between a sequence and a series?
A sequence is the ordered list of terms; a series is the sum of those terms. The calculator reports both the nth term of the sequence and the sum (series) of the first n terms.