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解答 - 几何数列

公比是：

r = 0.16363636363636364

r=0.16363636363636364

该系列的和是：

s = 64

s=64

此系列的通用形式是：

a_{n} = 55 \cdot {0.16363636363636364}^{n - 1}

a_n=55*0.16363636363636364^(n-1)

这个序列的第n项是：

55, 9, 1.4727272727272729, 0.24099173553719008, 0.039435011269722015, 0.006453001844136329, 0.0010559457563132175, 0.00017279112376034468, 2.827491116078367 E - 05, 4.626803644491874 E - 06

55,9,1.4727272727272729,0.24099173553719008,0.039435011269722015,0.006453001844136329,0.0010559457563132175,0.00017279112376034468,2.827491116078367E-05,4.626803644491874E-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：

$a_{2} a_{1} = \frac{9}{55} = 0.16363636363636364$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.16363636363636364$

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： $a = 55$ 、公比： $r = 0.16363636363636364$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 55 * ((1 - {0.16363636363636364}^{2}) / (1 - 0.16363636363636364))$

$s_{2} = 55 * ((1 - 0.026776859504132233) / (1 - 0.16363636363636364))$

$s_{2} = 55 * (0.9732231404958678 / (1 - 0.16363636363636364))$

$s_{2} = 55 * (0.9732231404958678 / 0.8363636363636364)$

$s_{2} = 55 \cdot 1.1636363636363636$

$s_{2} = 64$

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： $a = 55$ 和公比： $r = 0.16363636363636364$ 插入几何级数的公式：

$a_{n} = 55 \cdot {0.16363636363636364}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 55$

$a_{2} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{2 - 1} = 55 \cdot {0.16363636363636364}^{1} = 55 \cdot 0.16363636363636364 = 9$

$a_{3} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{3 - 1} = 55 \cdot {0.16363636363636364}^{2} = 55 \cdot 0.026776859504132233 = 1.4727272727272729$

$a_{4} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{4 - 1} = 55 \cdot {0.16363636363636364}^{3} = 55 \cdot 0.0043816679188580015 = 0.24099173553719008$

$a_{5} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{5 - 1} = 55 \cdot {0.16363636363636364}^{4} = 55 \cdot 0.0007170002049040366 = 0.039435011269722015$

$a_{6} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{6 - 1} = 55 \cdot {0.16363636363636364}^{5} = 55 \cdot 0.00011732730625702417 = 0.006453001844136329$

$a_{7} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{7 - 1} = 55 \cdot {0.16363636363636364}^{6} = 55 \cdot 1.919901375114941 E - 05 = 0.0010559457563132175$

$a_{8} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{8 - 1} = 55 \cdot {0.16363636363636364}^{7} = 55 \cdot 3.1416567956426308 E - 06 = 0.00017279112376034468$

$a_{9} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{9 - 1} = 55 \cdot {0.16363636363636364}^{8} = 55 \cdot 5.140892938324304 E - 07 = 2.827491116078367 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.16363636363636364}^{10 - 1} = 55 \cdot {0.16363636363636364}^{9} = 55 \cdot 8.412370262712498 E - 08 = 4.626803644491874 E - 06$

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几何数列