Mathematics · Precalculus
Finite Geometric Series Calculator
Calculate the sum of the first n terms of a finite geometric sequence.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Compute 3^5 = 243.
- Apply 2(1−243)/(1−3).
- Series sum = 242.
Problem → model → reason → result
What problem does this model solve?
Calculate the sum of the first n terms of a finite geometric sequence.
Why does the model apply?
Multiplying the series by r and subtracting cancels its middle terms, leaving a compact expression for the sum.
What assumptions does it make?
The entered values lie in the function's real domain, the stated sequence or function family matches the problem, and angle units are used consistently.
Formula
Sₙ = a₁(1−rⁿ)/(1−r), r ≠ 1
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
The first 5 terms starting at 2 with ratio 3 sum to 242.
Common mistake
When r=1 every term equals a₁, so the sum is simply na₁.
When does this model not apply?
A numerical function value does not by itself establish a trend outside the chosen domain, and finite sequences should not be treated automatically as infinite ones.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Geometric series do?
Calculate the sum of the first n terms of a finite geometric sequence.
How does the Geometric series work?
The calculator applies Sₙ = a₁(1−rⁿ)/(1−r), r ≠ 1. Multiplying the series by r and subtracting cancels its middle terms, leaving a compact expression for the sum.
What can I learn from the Geometric series?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.