Sequences
The nth term
The (n - 1) rather than n trips people constantly: the first term has had zero steps applied to it, so the last of n terms has had n - 1.
The Formula
an = a1 + (n - 1) x d
The (n - 1) rather than n trips people constantly: the first term has had zero steps applied to it, so the last of n terms has had n - 1.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a1 | First term | — | The starting value, before any step has been applied. |
| d | Common difference | — | Negative when the sequence decreases, zero when it is constant. |
| n | Term position being found | count | Must be a positive whole number for an ordinary series. |
What Each Symbol Means
a1
First term
The starting value, before any step has been applied.
d
Common difference
Negative when the sequence decreases, zero when it is constant.
ncount
Term position being found
Must be a positive whole number for an ordinary series.
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.