Sequences
The nth term
Each step applies one more factor of r, so the nth term carries n - 1 of them — the first term has none.
The Formula
an = a1 x r^(n - 1)
Each step applies one more factor of r, so the nth term carries n - 1 of them — the first term has none.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r | Common ratio | — | Term divided by previous term. Negative ratios produce alternating signs. |
| n | Position of the term | count | Must be a positive whole number. |
What Each Symbol Means
r
Common ratio
Term divided by previous term. Negative ratios produce alternating signs.
ncount
Position of the term
Must be a positive whole number.
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.