Sequences
Sum without knowing the last term
Substitute an = a1 + (n-1)d into the previous formula. Use this when you hold the step size rather than the endpoint.
The Formula
S = n/2 x (2a1 + (n - 1)d)
Substitute an = a1 + (n-1)d into the previous formula. Use this when you hold the step size rather than the endpoint.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| S | Sum of the first n terms | — | Numerically identical to the endpoint version. |
What Each Symbol Means
S
Sum of the first n terms
Numerically identical to the endpoint version.
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 an arithmetic 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 An Arithmetic Series, filed under Math. Every number the guide produces comes from substituting into this one line.