Number Sequence Calculator
Calculate various mathematical sequences including arithmetic, geometric, Fibonacci, triangular, and square number sequences.
Sequence Calculator
About Number Sequences
A number sequence is an ordered list of numbers that follows a specific pattern or rule. Understanding sequences is fundamental in mathematics, computer science, and many real-world applications.
Types of Sequences
- Arithmetic: Each term increases by a constant difference
- Geometric: Each term is multiplied by a constant ratio
- Fibonacci: Each term is the sum of the two preceding terms
- Triangular: Numbers representing triangular arrangements
- Square: Perfect square numbers (1, 4, 9, 16, ...)
Arithmetic Sequences
- Formula: aₙ = a₁ + (n-1)d
- Sum Formula: Sₙ = n/2 × (2a₁ + (n-1)d)
- Example: 2, 5, 8, 11, 14... (d = 3)
Geometric Sequences
- Formula: aₙ = a₁ × r^(n-1)
- Sum Formula: Sₙ = a₁(1-rⁿ)/(1-r) for r ≠ 1
- Example: 2, 6, 18, 54, 162... (r = 3)
Special Sequences
- Fibonacci: 0, 1, 1, 2, 3, 5, 8, 13, 21...
- Triangular: 1, 3, 6, 10, 15, 21, 28...
- Perfect Squares: 1, 4, 9, 16, 25, 36, 49...
- Prime Numbers: 2, 3, 5, 7, 11, 13, 17...
Applications
- Finance: Compound interest calculations
- Computer Science: Algorithm analysis, recursion
- Physics: Wave patterns, harmonic motion
- Biology: Population growth models
- Music: Harmonic series, frequency ratios