Enter at least 3 terms of a sequence to detect whether it is arithmetic or geometric, and find any term you need.
This tool identifies patterns in a number sequence and predicts the next terms, or generates sequences based on a defined rule (like arithmetic or geometric progressions). It's useful for math homework, pattern recognition exercises, and understanding sequence and series concepts.
An arithmetic sequence has a constant difference between consecutive terms (e.g., 2, 5, 8, 11 — difference of 3). A geometric sequence has a constant ratio between consecutive terms (e.g., 2, 6, 18, 54 — ratio of 3). The calculator identifies the pattern type and applies the corresponding formula to extend the sequence.
Enter a few terms of your number sequence, and the calculator identifies the pattern and predicts the next terms, or calculates a specific term number if you specify the rule.
Example 1 (arithmetic): The sequence 3, 7, 11, 15 has a common difference of 4, so the next term is 19.
Example 2 (geometric): The sequence 2, 4, 8, 16 has a common ratio of 2, so the next term is 32.
What's the difference between arithmetic and geometric sequences? Arithmetic sequences add or subtract a constant value between terms, while geometric sequences multiply or divide by a constant ratio between terms.
What is the formula for the nth term of an arithmetic sequence? aₙ = a₁ + (n-1)d, where a₁ is the first term, n is the term number, and d is the common difference.
What is the formula for the nth term of a geometric sequence? aₙ = a₁ × r^(n-1), where a₁ is the first term, n is the term number, and r is the common ratio.
Can this handle more complex sequences, like Fibonacci? Some sequence calculators can recognize special patterns like the Fibonacci sequence (where each term is the sum of the two preceding ones), though this requires different logic than simple arithmetic or geometric rules.
Why are number sequences important in math? They form the foundation for understanding series, limits, and later concepts in calculus, and they help develop pattern recognition and logical reasoning skills.