🔢Arithmetic Sequence Calculator

Calculate nth term and sum of arithmetic sequence from first term and common difference

First Term (a₁)

Common Difference (d)

Term Number (n)

How to Use the Arithmetic Sequence Calculator

An arithmetic sequence has a constant difference between consecutive terms. Enter the first term (a₁), common difference (d), and term number (n) to get the nth term and the sum of the first n terms instantly.

Key Formulas

nth term: a_n = a₁ + (n−1)d

Sum: S_n = n/2 × (a₁ + a_n) = n/2 × (2a₁ + (n−1)d)

Example

First term 3, difference 5: 3, 8, 13, 18, 23, … 10th term = 3 + 9×5 = 48. Sum of 10 terms = 10/2 × (3+48) = 255.

FAQ

Can the common difference be negative?

Yes. A negative difference creates a decreasing sequence. Example: first term 100, d = −10 gives 100, 90, 80, … The same formulas apply.

Does n have to be a whole number?

Yes. Term numbers are natural numbers (positive integers). Entering a decimal like 5.5 will show an error.