Number Sequence Calculator

Steps for Calculation

1. Input Values:
   • Enter the first term of the sequence (e.g., 1).
   • Enter the common difference (for arithmetic sequences) or common ratio (for geometric sequences) (e.g., 2).
   • Enter the number of terms you want in the sequence (e.g., 5).
2. Select Sequence Type:
   • Choose the type of sequence from the dropdown menu:
     • Arithmetic Sequence: Adds the common difference to each term.
     • Geometric Sequence: Multiplies each term by the common ratio.
3. Generate Sequence:
   • Click the Generate Sequence button to calculate the sequence.
4. View Result:
   • The generated sequence will be displayed below the button.

Detailed Description

• Arithmetic Sequence:
  • An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.
  • Formula: an=a1+(n−1)⋅dan​=a1​+(n−1)⋅d, where:
    • anan​ = nth term,
    • a1a1​ = first term,
    • dd = common difference,
    • nn = term number.
  • Example: For a1=1a1​=1, d=2d=2, and n=5n=5, the sequence is: 1, 3, 5, 7, 9.
• Geometric Sequence:
  • A geometric sequence is a sequence of numbers where the ratio between consecutive terms is constant.
  • Formula: an=a1⋅r(n−1)an​=a1​⋅r(n−1), where:
    • anan​ = nth term,
    • a1a1​ = first term,
    • rr = common ratio,
    • nn = term number.
  • Example: For a1=1a1​=1, r=2r=2, and n=5n=5, the sequence is: 1, 2, 4, 8, 16.