Geometric Series Sum
Calculate the sum of the first n terms of a geometric sequence.
How to use
- Enter first term a, term count n, and ratio r.
- Calculate to obtain the total of the first n terms.
Capabilities and scope
The calculator uses the finite geometric-series formula for a repeated multiplicative pattern.
How it works
For r≠1 it uses S_n=a(1−r^n)/(1−r); mathematically r=1 reduces to n×a.
Example
First term 1, ratio 2, and four terms sum to 1+2+4+8=15.
Useful for
- Total a sequence that multiplies each period
- Compute the finite total of a geometric progression
Before you use it
- Ratios extremely close to 1 can suffer floating-point cancellation.
Frequently asked questions
What if the ratio is exactly 1?
Mathematically all terms equal a and the sum is n×a; check this special case when interpreting the implementation.