Arithmetic Sequence Calculator
Generate an arithmetic sequence, sum it, or solve backwards, with formulas and steps
📐 参数输入
💡 输入即实时计算，支持小数。通项公式：an = a₁ + (n-1)d
请输入有效参数进行计算
About this tool
The arithmetic sequence calculator generates a sequence, sums its first n terms and can solve for a missing parameter:
- Generate: enter the first term a1, the common difference d and the count n to list the first n terms
- Sum: the partial sum Sn updates live
- Formulas: the nth term a_n = a1 + (n-1)d and the sum Sn = n(a1 + a_n)/2 are shown
- Solve backwards: given the first term, last term and count, recover the common difference
- Statistics: first term, last term, count, sum and average
Arithmetic sequence formulas
- Nth term: a_n = a1 + (n-1)d
- Sum: Sn = n times (a1 + a_n) / 2 = n times a1 + n(n-1)d/2
When to use it
- Sequence homework and study
- Checking answers to arithmetic sequence problems
- Fixed-increment or fixed-decrement schedules in finance
Formula reference
| Formula | Expression | Meaning |
|---|---|---|
| Nth term | a_n = a1 + (n-1)d | First term plus difference times count minus one |
| Sum | Sn = n(a1+a_n)/2 | Count times first plus last, divided by 2 |
| Sum, alternate | Sn = n a1 + n(n-1)d/2 | The same sum in another form |