1. What is Sequence Analysis?

Sequence analysis involves identifying patterns in ordered lists of numbers. This calculator detects common sequence types and finds their general formulas, allowing you to predict future terms.

2. How Does the Calculator Work?

The calculator analyzes the differences between terms to identify patterns:

Where:

• \( a_n \) — nth term of the sequence
• \( a_1 \) — First term
• \( d \) — Common difference (arithmetic)
• \( r \) — Common ratio (geometric)
• \( a, b, c \) — Coefficients (quadratic)

3. Types of Sequences

Arithmetic: Constant difference between terms (e.g., 2,5,8,11...)
Geometric: Constant ratio between terms (e.g., 3,6,12,24...)
Quadratic: Second differences are constant (e.g., 1,4,9,16...)
Other: Fibonacci, factorial, prime numbers, etc.

4. Using the Calculator

Tips: Enter at least 3-4 terms for accurate identification. Separate numbers with commas. The calculator works best with simple arithmetic, geometric, or quadratic sequences.

5. Frequently Asked Questions (FAQ)

Q1: How many terms do I need to enter?
A: Minimum 2 terms for arithmetic/geometric, 3 for quadratic. More terms increase accuracy.

Q2: What if my sequence isn't recognized?
A: The calculator may not detect complex patterns. Try entering more terms or check for alternative patterns.

Q3: Can it handle fractions/decimal numbers?
A: Yes, the calculator works with both integers and decimals.

Q4: What about recursive sequences?
A: This calculator focuses on explicit formulas. Recursive sequences (like Fibonacci) require different analysis.

Q5: Can it predict terms beyond the next two?
A: Once you have the formula, you can calculate any term by plugging in the term number (n).