1. Definition
A geometric sequence has a constant ratio q (q≠0) between successive terms; the nth term is a_n=a₁q^(n−1).
2. Formula & Notation
| a₁ | First term |
| q | Common ratio |
3. Properties & Laws
- a_n=a₁q^(n−1);
- q>1 grows (a₁>0), 0<q<1 decays;
- Geometric mean b²=ac;
- a_n=a_m·q^(n−m).
4. Steps
- Enter a₁, q, n;
- Click "Find Term";
- Or click "Load Example".
5. Worked Examples
Example: 1,2,4 (q=2) gives a_10=512.
6. Common Pitfalls
Exponent is n−1;
q≠0, a₁≠0;
Negative q alternates signs.