Number Sequence Calculator

Identify the patterns in your numbers with these steps:

Step 1: Enter the first few terms of your sequence separated by commas (e.g., 2, 5, 8, 11).

Step 2: The calculator will automatically detect if it is Arithmetic or Geometric.

Step 3: Enter the term number 'n' you want to find (e.g., the 100th term).

Step 4: Click "Calculate Sequence."

Step 5: Review the output. The calculator will provide: - The Common Difference (d) or Common Ratio (r). - The formula for the n-th term. - The value of the specific term you requested. - The Sum of the first 'n' terms (the series sum).

The two most common types of sequences are:

1. Arithmetic Sequence: Each term is found by adding a constant "difference" (d). Formula: aₙ = a₁ + (n-1)d Sum: Sₙ = (n/2)(a₁ + aₙ)

2. Geometric Sequence: Each term is found by multiplying by a constant "ratio" (r). Formula: aₙ = a₁ * r^(n-1) Sum: Sₙ = a₁(1 - rⁿ) / (1 - r)

Example (Arithmetic 2, 4, 6...): First term a₁ = 2, Difference d = 2. 10th term = 2 + (10-1)*2 = 20.

The Number Sequence Calculator is a powerful tool for recognizing trends and predicting future values. In finance, geometric sequences are used to calculate compound interest and investment growth. In physics, arithmetic sequences can model motion with constant acceleration. For students, this tool is an excellent way to check homework and visualize how a simple starting number and a rule can create vast sets of data. By providing the formulas and the partial sums, it helps bridge the gap between simple counting and advanced mathematical series.