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解答 - 几何数列

公比是：

r = 0.12727272727272726

r=0.12727272727272726

该系列的和是：

s = 186

s=186

此系列的通用形式是：

a_{n} = 165 \cdot {0.12727272727272726}^{n - 1}

a_n=165*0.12727272727272726^(n-1)

这个序列的第n项是：

165, 20.999999999999996, 2.672727272727272, 0.3401652892561982, 0.043293764087152506, 0.0055101154292739535, 0.0007012874182712305, 8.925476232542931 E - 05, 1.1359697023236457 E - 05, 1.4457796211391852 E - 06

165,20.999999999999996,2.672727272727272,0.3401652892561982,0.043293764087152506,0.0055101154292739535,0.0007012874182712305,8.925476232542931E-05,1.1359697023236457E-05,1.4457796211391852E-06

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：

$a_{2} a_{1} = \frac{21}{165} = 0.12727272727272726$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.12727272727272726$

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： $a = 165$ 、公比： $r = 0.12727272727272726$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 165 * ((1 - {0.12727272727272726}^{2}) / (1 - 0.12727272727272726))$

$s_{2} = 165 * ((1 - 0.01619834710743801) / (1 - 0.12727272727272726))$

$s_{2} = 165 * (0.9838016528925619 / (1 - 0.12727272727272726))$

$s_{2} = 165 * (0.9838016528925619 / 0.8727272727272728)$

$s_{2} = 165 \cdot 1.1272727272727272$

$s_{2} = 186$

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： $a = 165$ 和公比： $r = 0.12727272727272726$ 插入几何级数的公式：

$a_{n} = 165 \cdot {0.12727272727272726}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 165$

$a_{2} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{2 - 1} = 165 \cdot {0.12727272727272726}^{1} = 165 \cdot 0.12727272727272726 = 20.999999999999996$

$a_{3} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{3 - 1} = 165 \cdot {0.12727272727272726}^{2} = 165 \cdot 0.01619834710743801 = 2.672727272727272$

$a_{4} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{4 - 1} = 165 \cdot {0.12727272727272726}^{3} = 165 \cdot 0.0020616078136739286 = 0.3401652892561982$

$a_{5} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{5 - 1} = 165 \cdot {0.12727272727272726}^{4} = 165 \cdot 0.00026238644901304547 = 0.043293764087152506$

$a_{6} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{6 - 1} = 165 \cdot {0.12727272727272726}^{5} = 165 \cdot 3.339463896529669 E - 05 = 0.0055101154292739535$

$a_{7} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{7 - 1} = 165 \cdot {0.12727272727272726}^{6} = 165 \cdot 4.250226777401397 E - 06 = 0.0007012874182712305$

$a_{8} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{8 - 1} = 165 \cdot {0.12727272727272726}^{7} = 165 \cdot 5.409379534874504 E - 07 = 8.925476232542931 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{9 - 1} = 165 \cdot {0.12727272727272726}^{8} = 165 \cdot 6.88466486256755 E - 08 = 1.1359697023236457 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 165 \cdot {0.12727272727272726}^{10 - 1} = 165 \cdot {0.12727272727272726}^{9} = 165 \cdot 8.76230073417688 E - 09 = 1.4457796211391852 E - 06$

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几何数列