.png&w=3840&q=75)
.png&w=3840&q=75)
Number Sequence
Arithmetic and geometric sequences
How It Works
A number sequence is a list of numbers that follow a specific pattern. The two most common types are arithmetic sequences (constant difference) and geometric sequences (constant ratio).
A number sequence is a list of numbers that follow a specific pattern. In mathematics, a sequence is typically defined recursively or by a closed-form formula. An arithmetic sequence has a constant difference between consecutive terms. The nth term is given by a_n = a₁ + (n−1)d and the sum of the first n terms is S_n = n(a₁ + a_n)/2. A geometric sequence has a constant ratio between consecutive terms. The nth term is given by a_n = a₁ × r^(n−1) and the sum of the first n terms is S_n = a₁(1−r^n)/(1−r) for r ≠ 1.
Results
Enter values to see results
Quick Tips
- • Results update automatically as you type
- • Use Tab to navigate between fields
- • Press Enter to calculate