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 × r^(n - 1)
等比数列与指数级数通项计算器
根据 a_n = a₁ × r^(n - 1) 计算等比数列第 n 项、首项 a₁、公比 r 或项数 n。
a_n = a₁ × r^(n - 1)
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 Geometric Term
计算结果
Value of the progression at position n
0.00011.0000e+9
unit
Initial value at index n = 1
0.0011,000,000.00
unit
Constant multiplicative factor between terms
0.0520
unit
1-based index of the term
1100
unit
计算结果 · N-th Geometric Term (a_n)
1,536.00
分步代入计算过程
01Canonical Law: a_n = a₁ × r^(n - 1)
02Given Inputs (Base Units): a₁ = 3, r = 2, n = 10
03Solve for a_n (N-th Geometric Term): a_n = 1,536
A geometric progression multiplies each term by a constant non-zero common ratio r, generating exponential scaling governed by a_n = a₁ × r^(n - 1).
常见参考标准值
Finite Geometric Series SumS_n = a₁(1 - rⁿ) / (1 - r)
For a₁=3, r=2, n=10: S₁₀ = 3,069
Infinite Convergent Series (|r| < 1)S_∞ = a₁ / (1 - r)
Converges to a finite limit whenever -1 < r < 1
Geometric Mean of Adjacent Termsa_k = √(a_{k-1} × a_{k+1})
Logarithmic midpoint property
20 行数值对照表
N-th Geometric Term (a_n) · First Term (a₁)
| # | First Term (a₁) | N-th Geometric Term (a_n) | Δ % |
|---|---|---|---|
| 01 | 3 当前 | 1,536.00 | 0.00% |
| 02 | 7,237.00 | 3,705,344.48 | +241133.36% |
| 03 | 14,474.00 | 7,410,688.45 | +482366.70% |
| 04 | 21,711.00 | 11,116,032.42 | +723600.03% |
| 05 | 28,948.00 | 14,821,376.39 | +964833.36% |
| 06 | 36,185.00 | 18,526,720.36 | +1206066.69% |
| 07 | 43,422.00 | 22,232,064.33 | +1447300.02% |
| 08 | 50,659.00 | 25,937,408.30 | +1688533.35% |
| 09 | 57,896.00 | 29,642,752.27 | +1929766.68% |
| 10 | 65,133.00 | 33,348,096.24 | +2171000.02% |
| 11 | 72,370.00 | 37,053,440.21 | +2412233.35% |
| 12 | 79,607.00 | 40,758,784.17 | +2653466.68% |
| 13 | 86,844.00 | 44,464,128.14 | +2894700.01% |
| 14 | 94,081.00 | 48,169,472.11 | +3135933.34% |
| 15 | 101,318.00 | 51,874,816.08 | +3377166.67% |
| 16 | 108,555.00 | 55,580,160.05 | +3618400.00% |
| 17 | 115,792.00 | 59,285,504.02 | +3859633.33% |
| 18 | 123,029.00 | 62,990,847.99 | +4100866.67% |
| 19 | 130,266.00 | 66,696,191.96 | +4342100.00% |
| 20 | 137,503.00 | 70,401,535.93 | +4583333.33% |
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常见问题解答 (FAQ)
如何使用在线 等比数列与指数级数通项计算器 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 等比数列与指数级数通项计算器（基于关系式 a_n = a₁ × r^(n - 1)）。根据 a_n = a₁ × r^(n - 1) 计算等比数列第 n 项、首项 a₁、公比 r 或项数 n。
可以导出或打印 等比数列与指数级数通项计算器 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 等比数列与指数级数通项计算器 中的示例数据并从空白状态开始吗？+
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