Soma PG Finita Sₙ
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Sₙ = a(1−rⁿ)/(1−r)
About this calculator
This calculator determines the sum of the first n terms of a finite geometric progression. It uses the formula Sₙ = a₁·(1−rⁿ)/(1−r), where a₁ is the first term, r is the common ratio, and n is the number of terms. The tool is useful for solving geometric series problems in financial, physical, or mathematical contexts.
The operation is simple: you enter the first term, the common ratio, and the number of terms. The calculator applies the formula and returns the total sum. For ratios different from 1, the formula is valid; if r = 1, the sum is simply n·a₁, since all terms are equal.
Use this calculator for compound interest on equal installments, population growth at regular intervals, or any situation where a quantity multiplies by a constant factor each step. It is common in financial mathematics and sequences.
Caution: the formula assumes the progression is exactly geometric. Check that the ratio is constant between terms. Also, for r < 1, the sum converges to a limit as n approaches infinity, but here we only handle finite sums.
Frequently asked questions
What to do if the common ratio is 1?
If the ratio is 1, all terms are equal to the first. In that case, the sum is n times the first term, because the standard formula would have a zero denominator.
Does this calculator work for infinite progressions?
No, it only calculates the sum of a finite number of terms. For infinite progressions, use the limit formula when |r| < 1.
Can I use it for compound interest?
Yes, if you have a series of equal payments with geometric growth, such as in loans, the formula can be applied.
What is the difference between finite and infinite GP?
A finite GP has a limited number of terms; an infinite one continues indefinitely. The infinite sum only converges if the ratio is between -1 and 1.