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解答 - 几何数列

公比是：

r = 0.15584415584415584

r=0.15584415584415584

该系列的和是：

s = 89

s=89

此系列的通用形式是：

a_{n} = 77 \cdot {0.15584415584415584}^{n - 1}

a_n=77*0.15584415584415584^(n-1)

这个序列的第n项是：

77, 12, 1.87012987012987, 0.2914488109293304, 0.045420593911064476, 0.007078534116010048, 0.001103148173923644, 0.0001719191959361523, 2.679260196407568 E - 05, 4.1754704359598455 E - 06

77,12,1.87012987012987,0.2914488109293304,0.045420593911064476,0.007078534116010048,0.001103148173923644,0.0001719191959361523,2.679260196407568E-05,4.1754704359598455E-06

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：

$a_{2} a_{1} = \frac{12}{77} = 0.15584415584415584$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.15584415584415584$

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： $a = 77$ 、公比： $r = 0.15584415584415584$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 77 * ((1 - {0.15584415584415584}^{2}) / (1 - 0.15584415584415584))$

$s_{2} = 77 * ((1 - 0.024287400910777534) / (1 - 0.15584415584415584))$

$s_{2} = 77 * (0.9757125990892225 / (1 - 0.15584415584415584))$

$s_{2} = 77 * (0.9757125990892225 / 0.8441558441558441)$

$s_{2} = 77 \cdot 1.155844155844156$

$s_{2} = 89$

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： $a = 77$ 和公比： $r = 0.15584415584415584$ 插入几何级数的公式：

$a_{n} = 77 \cdot {0.15584415584415584}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 77$

$a_{2} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{2 - 1} = 77 \cdot {0.15584415584415584}^{1} = 77 \cdot 0.15584415584415584 = 12$

$a_{3} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{3 - 1} = 77 \cdot {0.15584415584415584}^{2} = 77 \cdot 0.024287400910777534 = 1.87012987012987$

$a_{4} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{4 - 1} = 77 \cdot {0.15584415584415584}^{3} = 77 \cdot 0.0037850494925887063 = 0.2914488109293304$

$a_{5} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{5 - 1} = 77 \cdot {0.15584415584415584}^{4} = 77 \cdot 0.0005898778430008374 = 0.045420593911064476$

$a_{6} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{6 - 1} = 77 \cdot {0.15584415584415584}^{5} = 77 \cdot 9.192901449363698 E - 05 = 0.007078534116010048$

$a_{7} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{7 - 1} = 77 \cdot {0.15584415584415584}^{6} = 77 \cdot 1.4326599661346024 E - 05 = 0.001103148173923644$

$a_{8} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{8 - 1} = 77 \cdot {0.15584415584415584}^{7} = 77 \cdot 2.23271683033964 E - 06 = 0.0001719191959361523$

$a_{9} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{9 - 1} = 77 \cdot {0.15584415584415584}^{8} = 77 \cdot 3.479558696633205 E - 07 = 2.679260196407568 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.15584415584415584}^{10 - 1} = 77 \cdot {0.15584415584415584}^{9} = 77 \cdot 5.4226888778699296 E - 08 = 4.1754704359598455 E - 06$

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几何数列