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解答 - 几何数列

公比是：

r = 0.18518518518518517

r=0.18518518518518517

该系列的和是：

s = 160

s=160

此系列的通用形式是：

a_{n} = 135 \cdot {0.18518518518518517}^{n - 1}

a_n=135*0.18518518518518517^(n-1)

这个序列的第n项是：

135, 25, 4.629629629629629, 0.8573388203017832, 0.1587664482040339, 0.02940119411185813, 0.0054446655762700235, 0.0010082714030129672, 0.0001867169264838828, 3.4577208608126444 E - 05

135,25,4.629629629629629,0.8573388203017832,0.1587664482040339,0.02940119411185813,0.0054446655762700235,0.0010082714030129672,0.0001867169264838828,3.4577208608126444E-05

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：

$a_{2} a_{1} = \frac{25}{135} = 0.18518518518518517$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.18518518518518517$

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： $a = 135$ 、公比： $r = 0.18518518518518517$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 135 * ((1 - {0.18518518518518517}^{2}) / (1 - 0.18518518518518517))$

$s_{2} = 135 * ((1 - 0.034293552812071325) / (1 - 0.18518518518518517))$

$s_{2} = 135 * (0.9657064471879286 / (1 - 0.18518518518518517))$

$s_{2} = 135 * (0.9657064471879286 / 0.8148148148148149)$

$s_{2} = 135 \cdot 1.1851851851851851$

$s_{2} = 160$

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： $a = 135$ 和公比： $r = 0.18518518518518517$ 插入几何级数的公式：

$a_{n} = 135 \cdot {0.18518518518518517}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 135$

$a_{2} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{2 - 1} = 135 \cdot {0.18518518518518517}^{1} = 135 \cdot 0.18518518518518517 = 25$

$a_{3} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{3 - 1} = 135 \cdot {0.18518518518518517}^{2} = 135 \cdot 0.034293552812071325 = 4.629629629629629$

$a_{4} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{4 - 1} = 135 \cdot {0.18518518518518517}^{3} = 135 \cdot 0.006350657928161357 = 0.8573388203017832$

$a_{5} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{5 - 1} = 135 \cdot {0.18518518518518517}^{4} = 135 \cdot 0.0011760477644743251 = 0.1587664482040339$

$a_{6} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{6 - 1} = 135 \cdot {0.18518518518518517}^{5} = 135 \cdot 0.00021778662305080095 = 0.02940119411185813$

$a_{7} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{7 - 1} = 135 \cdot {0.18518518518518517}^{6} = 135 \cdot 4.033085612051869 E - 05 = 0.0054446655762700235$

$a_{8} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{8 - 1} = 135 \cdot {0.18518518518518517}^{7} = 135 \cdot 7.468677059355313 E - 06 = 0.0010082714030129672$

$a_{9} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{9 - 1} = 135 \cdot {0.18518518518518517}^{8} = 135 \cdot 1.3830883443250578 E - 06 = 0.0001867169264838828$

$a_{10} = a_{1} \cdot r^{n - 1} = 135 \cdot {0.18518518518518517}^{10 - 1} = 135 \cdot {0.18518518518518517}^{9} = 135 \cdot 2.56127471171307 E - 07 = 3.4577208608126444 E - 05$

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几何数列