Arithmetic Sequence Calculator

An arithmetic sequence is a list of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference, denoted d. For example, 2, 5, 8, 11, 14 is an arithmetic sequence with first term a1 = 2 and common difference d = 3.

The nth term of an arithmetic sequence is aₙ = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the position of the term. This formula lets you find any term without calculating all previous terms.

The sum of the first n terms of an arithmetic sequence is Sₙ = n/2 * (a1 + aₙ), or equivalently Sₙ = n/2 * (2a1 + (n - 1)d). This formula comes from the fact that the sum of the first and last terms equals the sum of the second and second-to-last terms, and so on.

The common difference d is the fixed amount added to each term to get the next term. If d is positive, the sequence increases. If d is negative, the sequence decreases. If d = 0, all terms are identical.

Arithmetic sequences appear in many contexts: car depreciation (decreasing by a fixed amount yearly), stadium seating (rows spaced equally), payment plans (equal monthly payments), and temperature changes (rising a fixed amount per hour). Any situation with constant linear change follows an arithmetic pattern.