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解答 - 几何数列

公比是：

r = 0.1095890410958904

r=0.1095890410958904

该系列的和是：

s = 81

s=81

此系列的通用形式是：

a_{n} = 73 \cdot {0.1095890410958904}^{n - 1}

a_n=73*0.1095890410958904^(n-1)

这个序列的第n项是：

73, 8, 0.8767123287671232, 0.09607806342653405, 0.010529102841264005, 0.0011538742839741374, 0.00012645197632593286, 1.3857750830239216 E - 05, 1.5186576252316947 E - 06, 1.6642823290210354 E - 07

73,8,0.8767123287671232,0.09607806342653405,0.010529102841264005,0.0011538742839741374,0.00012645197632593286,1.3857750830239216E-05,1.5186576252316947E-06,1.6642823290210354E-07

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：

$a_{2} a_{1} = \frac{8}{73} = 0.1095890410958904$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.1095890410958904$

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： $a = 73$ 、公比： $r = 0.1095890410958904$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 73 * ((1 - {0.1095890410958904}^{2}) / (1 - 0.1095890410958904))$

$s_{2} = 73 * ((1 - 0.012009757928316756) / (1 - 0.1095890410958904))$

$s_{2} = 73 * (0.9879902420716833 / (1 - 0.1095890410958904))$

$s_{2} = 73 * (0.9879902420716833 / 0.8904109589041096)$

$s_{2} = 73 \cdot 1.1095890410958904$

$s_{2} = 81$

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： $a = 73$ 和公比： $r = 0.1095890410958904$ 插入几何级数的公式：

$a_{n} = 73 \cdot {0.1095890410958904}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 73$

$a_{2} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{2 - 1} = 73 \cdot {0.1095890410958904}^{1} = 73 \cdot 0.1095890410958904 = 8$

$a_{3} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{3 - 1} = 73 \cdot {0.1095890410958904}^{2} = 73 \cdot 0.012009757928316756 = 0.8767123287671232$

$a_{4} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{4 - 1} = 73 \cdot {0.1095890410958904}^{3} = 73 \cdot 0.0013161378551580006 = 0.09607806342653405$

$a_{5} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{5 - 1} = 73 \cdot {0.1095890410958904}^{4} = 73 \cdot 0.00014423428549676718 = 0.010529102841264005$

$a_{6} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{6 - 1} = 73 \cdot {0.1095890410958904}^{5} = 73 \cdot 1.5806497040741607 E - 05 = 0.0011538742839741374$

$a_{7} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{7 - 1} = 73 \cdot {0.1095890410958904}^{6} = 73 \cdot 1.7322188537799022 E - 06 = 0.00012645197632593286$

$a_{8} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{8 - 1} = 73 \cdot {0.1095890410958904}^{7} = 73 \cdot 1.8983220315396187 E - 07 = 1.3857750830239216 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{9 - 1} = 73 \cdot {0.1095890410958904}^{8} = 73 \cdot 2.0803529112762943 E - 08 = 1.5186576252316947 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 73 \cdot {0.1095890410958904}^{10 - 1} = 73 \cdot {0.1095890410958904}^{9} = 73 \cdot 2.2798388068781308 E - 09 = 1.6642823290210354 E - 07$

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几何数列