Sequence Calculator - Arithmetic and Geometric Sequences

A sequence is an ordered list of numbers following a specific pattern. Arithmetic sequences add a constant difference, geometric sequences multiply by a constant ratio, and Fibonacci sequences sum the two previous terms.

1. 1

   Select Sequence Type

   Choose arithmetic, geometric, or Fibonacci sequence

2. 2

   Enter First Term

   Input the starting value of the sequence

3. 3

   Enter Parameter

   For arithmetic, enter common difference; for geometric, enter common ratio

4. 4

   Specify Position

   Enter the term position and number of terms to display

5. 5

   View Results

   See the nth term value, sum, and sequence preview

• 1

  Arithmetic sequence: constant difference between consecutive terms

• 2

  Geometric sequence: constant ratio between consecutive terms

• 3

  Sum of arithmetic sequence: Sn = n/2 x (a1 + an)

• 4

  Infinite geometric sum exists only when |r| < 1

• Confusing arithmetic and geometric sequences - one adds, the other multiplies

• Using n instead of (n-1) in formulas - the first term has no difference or ratio applied

• Forgetting Fibonacci standard start values - usually begins with 0, 1 or 1, 1

• Calculating infinite sum when |r| >= 1 - series only converges if |r| < 1