Sequences
Sum of the first n terms
Subtracting the series multiplied by r cancels every middle term. Valid for any r except exactly 1.
The Formula
S = a1 (1 - r^n) / (1 - r)
Subtracting the series multiplied by r cancels every middle term. Valid for any r except exactly 1.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| S | Sum of n terms | — | Grows without bound when |r| is greater than 1. |
What Each Symbol Means
S
Sum of n terms
Grows without bound when |r| is greater than 1.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to find the sum of a geometric series page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Find The Sum Of A Geometric Series, filed under Math. Every number the guide produces comes from substituting into this one line.