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解答 - 几何数列

公比是：

r = 0.017045454545454544

r=0.017045454545454544

该系列的和是：

s = 179

s=179

此系列的通用形式是：

a_{n} = 176 \cdot {0.017045454545454544}^{n - 1}

a_n=176*0.017045454545454544^(n-1)

这个序列的第n项是：

176, 3, 0.051136363636363626, 0.0008716425619834708, 1.4857543670172799 E - 05, 2.532535852870363 E - 07, 4.316822476483573 E - 09, 7.358220130369726 E - 11, 1.2542420676766577 E - 12, 2.1379126153579394 E - 14

176,3,0.051136363636363626,0.0008716425619834708,1.4857543670172799E-05,2.532535852870363E-07,4.316822476483573E-09,7.358220130369726E-11,1.2542420676766577E-12,2.1379126153579394E-14

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{3}{176} = 0.017045454545454544$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.017045454545454544$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = 176$ 、公比： $r = 0.017045454545454544$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 176 * ((1 - {0.017045454545454544}^{2}) / (1 - 0.017045454545454544))$

$s_{2} = 176 * ((1 - 0.000290547520661157) / (1 - 0.017045454545454544))$

$s_{2} = 176 * (0.9997094524793388 / (1 - 0.017045454545454544))$

$s_{2} = 176 * (0.9997094524793388 / 0.9829545454545454)$

$s_{2} = 176 \cdot 1.0170454545454546$

$s_{2} = 179$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = 176$ 和公比： $r = 0.017045454545454544$ 插入几何级数的公式：

$a_{n} = 176 \cdot {0.017045454545454544}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 176$

$a_{2} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{2 - 1} = 176 \cdot {0.017045454545454544}^{1} = 176 \cdot 0.017045454545454544 = 3$

$a_{3} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{3 - 1} = 176 \cdot {0.017045454545454544}^{2} = 176 \cdot 0.000290547520661157 = 0.051136363636363626$

$a_{4} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{4 - 1} = 176 \cdot {0.017045454545454544}^{3} = 176 \cdot 4.952514556724266 E - 06 = 0.0008716425619834708$

$a_{5} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{5 - 1} = 176 \cdot {0.017045454545454544}^{4} = 176 \cdot 8.441786176234545 E - 08 = 1.4857543670172799 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{6 - 1} = 176 \cdot {0.017045454545454544}^{5} = 176 \cdot 1.4389408254945244 E - 09 = 2.532535852870363 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{7 - 1} = 176 \cdot {0.017045454545454544}^{6} = 176 \cdot 2.4527400434565755 E - 11 = 4.316822476483573 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{8 - 1} = 176 \cdot {0.017045454545454544}^{7} = 176 \cdot 4.1808068922555264 E - 13 = 7.358220130369726 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{9 - 1} = 176 \cdot {0.017045454545454544}^{8} = 176 \cdot 7.126375384526465 E - 15 = 1.2542420676766577 E - 12$

$a_{10} = a_{1} \cdot r^{n - 1} = 176 \cdot {0.017045454545454544}^{10 - 1} = 176 \cdot {0.017045454545454544}^{9} = 176 \cdot 1.21472307690792 E - 16 = 2.1379126153579394 E - 14$

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几何数列