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解答 - 几何数列

公比是：

r = 0.10526315789473684

r=0.10526315789473684

该系列的和是：

s = 20

s=20

此系列的通用形式是：

a_{n} = 19 \cdot {0.10526315789473684}^{n - 1}

a_n=19*0.10526315789473684^(n-1)

这个序列的第n项是：

19, 2, 0.21052631578947364, 0.022160664819944595, 0.0023327015599941677, 0.00024554753263096503, 2.5847108697996318 E - 05, 2.720748283999612 E - 06, 2.8639455621048543 E - 07, 3.0146795390577416 E - 08

19,2,0.21052631578947364,0.022160664819944595,0.0023327015599941677,0.00024554753263096503,2.5847108697996318E-05,2.720748283999612E-06,2.8639455621048543E-07,3.0146795390577416E-08

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：

$a_{2} a_{1} = \frac{2}{19} = 0.10526315789473684$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.10526315789473684$

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： $a = 19$ 、公比： $r = 0.10526315789473684$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 19 * ((1 - {0.10526315789473684}^{2}) / (1 - 0.10526315789473684))$

$s_{2} = 19 * ((1 - 0.011080332409972297) / (1 - 0.10526315789473684))$

$s_{2} = 19 * (0.9889196675900277 / (1 - 0.10526315789473684))$

$s_{2} = 19 * (0.9889196675900277 / 0.8947368421052632)$

$s_{2} = 19 \cdot 1.1052631578947367$

$s_{2} = 20.999999999999996$

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： $a = 19$ 和公比： $r = 0.10526315789473684$ 插入几何级数的公式：

$a_{n} = 19 \cdot {0.10526315789473684}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 19$

$a_{2} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{2 - 1} = 19 \cdot {0.10526315789473684}^{1} = 19 \cdot 0.10526315789473684 = 2$

$a_{3} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{3 - 1} = 19 \cdot {0.10526315789473684}^{2} = 19 \cdot 0.011080332409972297 = 0.21052631578947364$

$a_{4} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{4 - 1} = 19 \cdot {0.10526315789473684}^{3} = 19 \cdot 0.0011663507799970839 = 0.022160664819944595$

$a_{5} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{5 - 1} = 19 \cdot {0.10526315789473684}^{4} = 19 \cdot 0.00012277376631548252 = 0.0023327015599941677$

$a_{6} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{6 - 1} = 19 \cdot {0.10526315789473684}^{5} = 19 \cdot 1.2923554348998159 E - 05 = 0.00024554753263096503$

$a_{7} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{7 - 1} = 19 \cdot {0.10526315789473684}^{6} = 19 \cdot 1.3603741419998062 E - 06 = 2.5847108697996318 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{8 - 1} = 19 \cdot {0.10526315789473684}^{7} = 19 \cdot 1.4319727810524274 E - 07 = 2.720748283999612 E - 06$

$a_{9} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{9 - 1} = 19 \cdot {0.10526315789473684}^{8} = 19 \cdot 1.5073397695288708 E - 08 = 2.8639455621048543 E - 07$

$a_{10} = a_{1} \cdot r^{n - 1} = 19 \cdot {0.10526315789473684}^{10 - 1} = 19 \cdot {0.10526315789473684}^{9} = 19 \cdot 1.5866734416093377 E - 09 = 3.0146795390577416 E - 08$

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几何数列