Geometric Progression Calculator
Calculate the nth term, sum of terms, and common ratio of a geometric sequence with an interactive exponential growth graph.
About
Geometric progressions model phenomena like population growth, compound interest, and radioactive decay. Engineers and financial analysts use these sequences to predict future values based on a constant multiplication factor. A small change in the common ratio results in massive differences over time. This tool computes the specific term and the cumulative sum for any defined sequence. It generates a visual plot to identify divergence or convergence immediately.
Formulas
The value of the n-th term is calculated using the initial term and the ratio raised to the power of n minus one.
The sum of the first n terms depends on whether the ratio is equal to one.
Reference Data
| Parameter | Symbol | Definition | Constraint |
|---|---|---|---|
| First Term | a1 | Initial value of the sequence | a1 ≠ 0 |
| Common Ratio | r | Factor between consecutive terms | r ∞ R |
| Term Position | n | Integer position of the term | n ≥ 1 |
| General Term | an | Value at position n | Calculated |
| Series Sum | Sn | Sum of first n terms | Finite if r ≠ 1 |