Sequence Calculator
Generate arithmetic or geometric sequences and get their nth term and sum.
Sequence Calculator
Generate arithmetic or geometric sequences and get their nth term and sum.
How to use the Sequence Calculator
- Choose "Arithmetic" or "Geometric".
- Enter the first term, common difference (or ratio), and number of terms.
- Click Calculate.
Formula
Arithmetic: aₙ = a₁ + (n−1)d
Sₙ = n/2 × (2a₁ + (n−1)d)
Geometric: aₙ = a₁ × r^(n−1)
Sₙ = a₁(rⁿ−1)/(r−1) if r≠1
Example
Arithmetic: a₁=3, d=5, n=6. Sequence: 3, 8, 13, 18, 23, 28. Sum = 93.
Step-by-step calculation
- Terms: 3, 3+5=8, 8+5=13, 13+5=18, 18+5=23, 23+5=28.
- 6th term: 3 + 5×5 = 28.
- Sum: 6/2 × (6+25) = 3 × 31 = 93.
Real-world uses
- Financial planning (monthly savings).
- Physics (constant acceleration).
- Computer science (loop analysis).
Common mistakes
- Confusing the common difference (arithmetic) with the common ratio (geometric).
- Using the wrong formula for geometric sum when r=1.
- Requesting too many terms (display is limited to 30).
Frequently asked questions
What is the difference between arithmetic and geometric?
Arithmetic adds a constant. Geometric multiplies by a constant.
What if the geometric ratio is 1?
All terms equal a₁. Sum = a₁ × n.
How many terms can I generate?
Up to 500 terms. The preview shows up to 30, with the sum and nth term always calculated.