03 // 双向 STEM 与金融计算器 // 代数、几何、三角与数列计算器a_n = a₁ + (n - 1) × d
等差数列通项与第 N 项计算器
利用通项公式 a_n = a₁ + (n - 1)d 求解第 n 项数值、首项 a₁、项数序号 n 或公差 d。
a_n = a₁ + (n - 1) × d
选择要计算的未知量（或直接在任意输入框中输入数值）：当前求解: a_n — N-th Term Value
计算结果
Value of the sequence at position n
-100,000.00100,000.00
unit
Starting value at index n = 1
-100,000.00100,000.00
unit
1-based index of the term
110,000.00
unit
Constant step added between consecutive terms
-1,000.001,000.00
unit
计算结果 · N-th Term Value (a_n)
100
分步代入计算过程
01Canonical Law: a_n = a₁ + (n - 1) × d
02Given Inputs (Base Units): a₁ = 5, n = 20, d = 5
03Solve for a_n (N-th Term Value): a_n = 100
An arithmetic progression advances by adding a constant common difference d to each preceding term, placing the n-th term at a_n = a₁ + (n - 1) × d.
常见参考标准值
Gauss Partial Sum (S_n)S_n = (n / 2) × (a₁ + a_n)
For default (a₁=5, a₂₀=100, n=20), S₂₀ = 1,050
Arithmetic Mean of Endpointsa_mid = (a₁ + a_n) / 2
Average of all terms equals average of first and last
Linear Function Equivalencef(n) = d·n + (a₁ - d)
Discrete linear slope d
20 行数值对照表
N-th Term Value (a_n) · First Term (a₁)
| # | First Term (a₁) | N-th Term Value (a_n) | Δ % |
|---|---|---|---|
| 01 | -22,495.00 | -22,400.00 | -22500.00% |
| 02 | -19,863.42 | -19,768.42 | -19868.42% |
| 03 | -17,231.84 | -17,136.84 | -17236.84% |
| 04 | -14,600.26 | -14,505.26 | -14605.26% |
| 05 | -11,968.68 | -11,873.68 | -11973.68% |
| 06 | -9,337.11 | -9,242.11 | -9342.11% |
| 07 | -6,705.53 | -6,610.53 | -6710.53% |
| 08 | -4,073.95 | -3,978.95 | -4078.95% |
| 09 | -1,442.37 | -1,347.37 | -1447.37% |
| 10 | 5 当前 | 100 | 0.00% |
| 11 | 3,820.79 | 3,915.79 | +3815.79% |
| 12 | 6,452.37 | 6,547.37 | +6447.37% |
| 13 | 9,083.95 | 9,178.95 | +9078.95% |
| 14 | 11,715.53 | 11,810.53 | +11710.53% |
| 15 | 14,347.11 | 14,442.11 | +14342.11% |
| 16 | 16,978.68 | 17,073.68 | +16973.68% |
| 17 | 19,610.26 | 19,705.26 | +19605.26% |
| 18 | 22,241.84 | 22,336.84 | +22236.84% |
| 19 | 24,873.42 | 24,968.42 | +24868.42% |
| 20 | 27,505.00 | 27,600.00 | +27500.00% |
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常见问题解答 (FAQ)
如何使用在线 等差数列通项与第 N 项计算器 工具？+
输入已知参数或拖动滑块，即可在浏览器中实时计算并可视化 等差数列通项与第 N 项计算器（基于关系式 a_n = a₁ + (n - 1) × d）。利用通项公式 a_n = a₁ + (n - 1)d 求解第 n 项数值、首项 a₁、项数序号 n 或公差 d。
可以导出或打印 等差数列通项与第 N 项计算器 的结果吗？+
可以。支持一键复制数据、打印计算工作表或导出高清 SVG、PNG 和 CSV 文件。
我可以清空 等差数列通项与第 N 项计算器 中的示例数据并从空白状态开始吗？+
可以。点击工具顶部的“清空 / 空白开始”按钮即可重置所有输入项，随时也可一键重新加载示例数据。