Sequences
Sum from the two ends
Pair the series with its reverse: every column sums to a1 + an, there are n columns across both rows, so one row is half.
The Formula
S = n/2 x (a1 + an)
Pair the series with its reverse: every column sums to a1 + an, there are n columns across both rows, so one row is half.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| an | Last term | — | Compute it first if you were not given it directly. |
| S | Sum of all n terms | — | Equal to n multiplied by the average term. |
What Each Symbol Means
an
Last term
Compute it first if you were not given it directly.
S
Sum of all n terms
Equal to n multiplied by the average term.
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.