Arithmetic Progression Calculator
Calculate the n-th term and sum of an arithmetic progression. Enter the first term, common difference, and term number to get results with formulas.
aₙ = a₁ + (n−1)d
How to Use the Arithmetic Progression Calculator
- Enter the numbers or values in the input fields.
- The result is calculated and displayed automatically.
- Review the step-by-step solution or detailed breakdown.
- Copy the result or adjust inputs for a new calculation.
Referência Rápida
| De | Para |
|---|---|
| 2 + 3 | 5 |
| 12 × 12 | 144 |
| √144 | 12 |
| 2¹⁰ | 1,024 |
| π | 3.14159 |
| e | 2.71828 |
Casos de Uso
- •Checking homework or exam answers quickly and accurately.
- •Verifying manual calculations in professional or academic work.
- •Learning mathematical concepts with instant visual feedback.
- •Performing quick computations during meetings or presentations.
Fórmula
An arithmetic progression has a constant difference d between consecutive terms. The n-th term: aₙ = a₁ + (n−1)d. Sum of first n terms: Sₙ = n·(a₁ + aₙ)/2.
Perguntas Frequentes
What is an arithmetic progression?
An arithmetic progression (AP) is a sequence where each term after the first is obtained by adding a constant value d (the common difference) to the previous term. Example: 2, 5, 8, 11, ... with d = 3.
How do I find the sum of an arithmetic series?
The sum of the first n terms is Sₙ = n·(a₁ + aₙ)/2, or equivalently Sₙ = n·(2a₁ + (n−1)d)/2. It is the average of the first and last term, multiplied by the number of terms.
Can the common difference be negative?
Yes. A negative common difference produces a decreasing arithmetic progression, for example: 20, 17, 14, 11, ... with d = −3.