Arithmetic Sequence Calculator

The Arithmetic Sequence Calculator computes key properties of an arithmetic sequence from three inputs: the first term (a1), common difference (d), and number of terms (n). It displays both the general term formula and multiple forms of the sum formula, making it useful for learning and checking arithmetic progression problems.

An arithmetic sequence is a series where consecutive terms have a constant difference. For example, "2, 5, 8, 11, 14, …" has first term 2 and common difference 3. The nth term is a_n = a1 + (n-1)d, and the sum can be calculated as S_n = n(a1 + a_n)/2 or alternatively as S_n = na1 + n(n-1)d/2. By showing both formulas, this tool helps you understand the deeper structure of arithmetic sequences.

Key features include automatic calculation of the nth term value, computation of the sum S_n from first term through nth term, display of both the general term formula and sum calculation formulas in concrete form, listing of each term up to 50 terms, and support for decimals and negative numbers across a wide range of sequence patterns.

This tool is useful for high school and university students studying arithmetic sequences, test-takers checking entrance or certification exam problems, engineers and programmers confirming arithmetic sequence values for statistics and algorithms, and anyone wanting to visualize sequence properties. Calculations run in your browser with no installation required.

For sequences with a constant ratio, use the [Geometric Sequence Calculator](/en/calc/geometric-sequence/). To inspect Fibonacci numbers, use the [Fibonacci Sequence Calculator](/en/calc/fibonacci-sequence/). For related algebra checks, [Quadratic Equation Solver](/en/calc/quadratic-equation/) and [Simultaneous Equations Solver](/en/calc/simultaneous-equations/) are also useful.