Number Sequence Calculator — Find Patterns & nth Term

Identifying and Extending Number Sequences

A number sequence is an ordered list of numbers that follows a specific pattern or rule. This calculator identifies whether a given sequence is arithmetic (constant difference between terms), geometric (constant ratio between terms), or follows another recognizable pattern. Once the pattern is identified, it calculates subsequent terms, provides the general formula, and computes the sum of the sequence.

An arithmetic sequence has a common difference d between consecutive terms, with the general formula a_n = a_1 + (n-1)d. For example, 2, 5, 8, 11 has d = 3. A geometric sequence has a common ratio r, with the formula a_n = a_1 * r^(n-1). For example, 3, 6, 12, 24 has r = 2. The calculator also recognizes quadratic sequences (where the second differences are constant), Fibonacci-like sequences, and other common patterns by analyzing the differences and ratios between consecutive terms.

Number sequences appear throughout mathematics, science, and finance. Arithmetic sequences model situations with constant growth, like monthly savings contributions. Geometric sequences describe exponential phenomena like compound interest, population growth, and radioactive decay. Pattern recognition in sequences is a fundamental skill tested in standardized exams and used in data analysis to identify trends. This calculator is useful for students studying series and sequences, teachers creating problem sets, and anyone who needs to extend or analyze a numerical pattern.