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解答 - 几何数列

公比是：

r = 0.6873015873015873

r=0.6873015873015873

该系列的和是：

s = 2125

s=2125

此系列的通用形式是：

a_{n} = 1260 \cdot {0.6873015873015873}^{n - 1}

a_n=1260*0.6873015873015873^(n-1)

这个序列的第n项是：

1260, 866, 595.2031746031746, 409.08408667170573, 281.16414210928343, 193.24456116399958, 132.8172936254156, 91.28553672984913, 62.74069429210265, 43.12177877536579

1260,866,595.2031746031746,409.08408667170573,281.16414210928343,193.24456116399958,132.8172936254156,91.28553672984913,62.74069429210265,43.12177877536579

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：

$a_{2} a_{1} = \frac{866}{1260} = 0.6873015873015873$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.6873015873015873$

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： $a = 1, 260$ 、公比： $r = 0.6873015873015873$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1260 * ((1 - {0.6873015873015873}^{2}) / (1 - 0.6873015873015873))$

$s_{2} = 1260 * ((1 - 0.4723834719072814) / (1 - 0.6873015873015873))$

$s_{2} = 1260 * (0.5276165280927185 / (1 - 0.6873015873015873))$

$s_{2} = 1260 * (0.5276165280927185 / 0.3126984126984127)$

$s_{2} = 1260 \cdot 1.687301587301587$

$s_{2} = 2125.9999999999995$

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： $a = 1, 260$ 和公比： $r = 0.6873015873015873$ 插入几何级数的公式：

$a_{n} = 1260 \cdot {0.6873015873015873}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1260$

$a_{2} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{2 - 1} = 1260 \cdot {0.6873015873015873}^{1} = 1260 \cdot 0.6873015873015873 = 866$

$a_{3} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{3 - 1} = 1260 \cdot {0.6873015873015873}^{2} = 1260 \cdot 0.4723834719072814 = 595.2031746031746$

$a_{4} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{4 - 1} = 1260 \cdot {0.6873015873015873}^{3} = 1260 \cdot 0.3246699100569093 = 409.08408667170573$

$a_{5} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{5 - 1} = 1260 \cdot {0.6873015873015873}^{4} = 1260 \cdot 0.22314614453117734 = 281.16414210928343$

$a_{6} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{6 - 1} = 1260 \cdot {0.6873015873015873}^{5} = 1260 \cdot 0.1533686993365076 = 193.24456116399958$

$a_{7} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{7 - 1} = 1260 \cdot {0.6873015873015873}^{6} = 1260 \cdot 0.10541055049636158 = 132.8172936254156$

$a_{8} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{8 - 1} = 1260 \cdot {0.6873015873015873}^{7} = 1260 \cdot 0.07244883867448343 = 91.28553672984913$

$a_{9} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{9 - 1} = 1260 \cdot {0.6873015873015873}^{8} = 1260 \cdot 0.04979420181912909 = 62.74069429210265$

$a_{10} = a_{1} \cdot r^{n - 1} = 1260 \cdot {0.6873015873015873}^{10 - 1} = 1260 \cdot {0.6873015873015873}^{9} = 1260 \cdot 0.03422363394870301 = 43.12177877536579$

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