Calculadora de Progressão Aritmética

The Arithmetic Progression (AP) Calculator is an online tool that determines the general term and the sum of the first n terms of a numerical sequence where the difference between consecutive terms is constant. To use it, you enter the first term (a₁), the common difference (r), and the number of terms (n). The calculator then applies the general term formula aₙ = a₁ + (n−1)·r to find any desired term, and the sum formula Sₙ = n·(a₁ + aₙ)/2 to calculate the total sum of the n terms. The process is automatic and provides instant results.

This calculator is useful in various practical situations, such as financial planning to calculate fixed installments of a loan, analyzing linear growth (e.g., constant monthly savings), or solving basic math problems and exams. For example, when simulating savings where you deposit R$ 100 in the first month and increase by R$ 20 each month, the AP helps predict the balance after 12 months. It is also applied in engineering to model staircases or uniform load distributions.

Important precautions: ensure the sequence is truly an AP (constant difference). The calculator assumes the common difference r is fixed; if there are variations, the result will be incorrect. Also, check that the number of terms n is correct, as common mistakes include counting the first term as term 0. For decreasing sequences, the common difference can be negative. The tool does not handle geometric progressions or other types of sequences.