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解答 - 几何数列

公比是：

r = 0.8990990990990991

r=0.8990990990990991

该系列的和是：

s = 1053

s=1053

此系列的通用形式是：

a_{n} = 555 \cdot {0.8990990990990991}^{n - 1}

a_n=555*0.8990990990990991^(n-1)

这个序列的第n项是：

555, 499, 448.6504504504505, 403.381215810405, 362.67968772863446, 326.0849804983578, 293.18271219582084, 263.600312406693, 237.00280340709872, 213.08900702728337

555,499,448.6504504504505,403.381215810405,362.67968772863446,326.0849804983578,293.18271219582084,263.600312406693,237.00280340709872,213.08900702728337

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：

$a_{2} a_{1} = \frac{499}{555} = 0.8990990990990991$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.8990990990990991$

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： $a = 555$ 、公比： $r = 0.8990990990990991$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 555 * ((1 - {0.8990990990990991}^{2}) / (1 - 0.8990990990990991))$

$s_{2} = 555 * ((1 - 0.8083791900008117) / (1 - 0.8990990990990991))$

$s_{2} = 555 * (0.1916208099991883 / (1 - 0.8990990990990991))$

$s_{2} = 555 * (0.1916208099991883 / 0.10090090090090087)$

$s_{2} = 555 \cdot 1.8990990990990988$

$s_{2} = 1053.9999999999998$

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： $a = 555$ 和公比： $r = 0.8990990990990991$ 插入几何级数的公式：

$a_{n} = 555 \cdot {0.8990990990990991}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 555$

$a_{2} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{2 - 1} = 555 \cdot {0.8990990990990991}^{1} = 555 \cdot 0.8990990990990991 = 499$

$a_{3} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{3 - 1} = 555 \cdot {0.8990990990990991}^{2} = 555 \cdot 0.8083791900008117 = 448.6504504504505$

$a_{4} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{4 - 1} = 555 \cdot {0.8990990990990991}^{3} = 555 \cdot 0.7268130014601892 = 403.381215810405$

$a_{5} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{5 - 1} = 555 \cdot {0.8990990990990991}^{4} = 555 \cdot 0.6534769148263684 = 362.67968772863446$

$a_{6} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{6 - 1} = 555 \cdot {0.8990990990990991}^{5} = 555 \cdot 0.5875405054024465 = 326.0849804983578$

$a_{7} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{7 - 1} = 555 \cdot {0.8990990990990991}^{6} = 555 \cdot 0.5282571390915691 = 293.18271219582084$

$a_{8} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{8 - 1} = 555 \cdot {0.8990990990990991}^{7} = 555 \cdot 0.47495551784989726 = 263.600312406693$

$a_{9} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{9 - 1} = 555 \cdot {0.8990990990990991}^{8} = 555 \cdot 0.4270320782109887 = 237.00280340709872$

$a_{10} = a_{1} \cdot r^{n - 1} = 555 \cdot {0.8990990990990991}^{10 - 1} = 555 \cdot {0.8990990990990991}^{9} = 555 \cdot 0.383944156805916 = 213.08900702728337$

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