Geometric Sequence Calculator
Generate a geometric sequence, sum it, or solve backwards, with formulas and steps
📐 参数输入
💡 输入即实时计算。通项公式：an = a₁ × r(n-1)
请输入有效参数进行计算
About this tool
The geometric sequence calculator generates a sequence, sums its first n terms and can solve for a missing parameter:
- Generate: enter the first term a1, the ratio r and the count n to list the first n terms
- Sum: the partial sum Sn updates live
- Formulas: the nth term a_n = a1 times r^(n-1) and the sum formula are shown
- Edge case: r = 1 is handled separately
- Solve backwards: given the first term, last term and count, recover the ratio
Geometric sequence formulas
- Nth term: a_n = a1 times r^(n-1)
- Sum when r is not 1: Sn = a1 times (1 - r^n) / (1 - r)
- Sum when r = 1: Sn = n times a1
When to use it
- Sequence homework and study
- Compound interest in finance
- Analysing geometric growth
Formula reference
| Formula | Expression |
|---|---|
| Nth term | a_n = a1 times r^(n-1) |
| Sum, r not 1 | Sn = a1(1-r^n)/(1-r) |
| Sum, r = 1 | Sn = n times a1 |