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解答 - 几何数列

公比是：

r = 0.11864406779661017

r=0.11864406779661017

该系列的和是：

s = 66

s=66

此系列的通用形式是：

a_{n} = 59 \cdot {0.11864406779661017}^{n - 1}

a_n=59*0.11864406779661017^(n-1)

这个序列的第n项是：

59, 7, 0.8305084745762713, 0.09853490376328641, 0.011690581802423813, 0.001387018179948588, 0.00016456147897695112, 1.952424326845183 E - 05, 2.3164356420197086 E - 06, 2.7483134735827053 E - 07

59,7,0.8305084745762713,0.09853490376328641,0.011690581802423813,0.001387018179948588,0.00016456147897695112,1.952424326845183E-05,2.3164356420197086E-06,2.7483134735827053E-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：

$a_{2} a_{1} = \frac{7}{59} = 0.11864406779661017$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.11864406779661017$

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： $a = 59$ 、公比： $r = 0.11864406779661017$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 59 * ((1 - {0.11864406779661017}^{2}) / (1 - 0.11864406779661017))$

$s_{2} = 59 * ((1 - 0.014076414823326631) / (1 - 0.11864406779661017))$

$s_{2} = 59 * (0.9859235851766733 / (1 - 0.11864406779661017))$

$s_{2} = 59 * (0.9859235851766733 / 0.8813559322033898)$

$s_{2} = 59 \cdot 1.11864406779661$

$s_{2} = 66$

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： $a = 59$ 和公比： $r = 0.11864406779661017$ 插入几何级数的公式：

$a_{n} = 59 \cdot {0.11864406779661017}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 59$

$a_{2} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{2 - 1} = 59 \cdot {0.11864406779661017}^{1} = 59 \cdot 0.11864406779661017 = 7$

$a_{3} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{3 - 1} = 59 \cdot {0.11864406779661017}^{2} = 59 \cdot 0.014076414823326631 = 0.8305084745762713$

$a_{4} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{4 - 1} = 59 \cdot {0.11864406779661017}^{3} = 59 \cdot 0.0016700831146319731 = 0.09853490376328641$

$a_{5} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{5 - 1} = 59 \cdot {0.11864406779661017}^{4} = 59 \cdot 0.00019814545427836972 = 0.011690581802423813$

$a_{6} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{6 - 1} = 59 \cdot {0.11864406779661017}^{5} = 59 \cdot 2.3508782710993017 E - 05 = 0.001387018179948588$

$a_{7} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{7 - 1} = 59 \cdot {0.11864406779661017}^{6} = 59 \cdot 2.7891776097788327 E - 06 = 0.00016456147897695112$

$a_{8} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{8 - 1} = 59 \cdot {0.11864406779661017}^{7} = 59 \cdot 3.309193774313869 E - 07 = 1.952424326845183 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{9 - 1} = 59 \cdot {0.11864406779661017}^{8} = 59 \cdot 3.92616210511815 E - 08 = 2.3164356420197086 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 59 \cdot {0.11864406779661017}^{10 - 1} = 59 \cdot {0.11864406779661017}^{9} = 59 \cdot 4.658158429801195 E - 09 = 2.7483134735827053 E - 07$

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几何数列