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解答 - 几何数列

公比是：

r = 0.024509803921568627

r=0.024509803921568627

该系列的和是：

s = 1881

s=1881

此系列的通用形式是：

a_{n} = 1836 \cdot {0.024509803921568627}^{n - 1}

a_n=1836*0.024509803921568627^(n-1)

这个序列的第n项是：

1836, 45, 1.102941176470588, 0.027032871972318337, 0.0006625703914783906, 1.623947037937232 E - 05, 3.9802623478853724 E - 07, 9.755544970307284 E - 09, 2.391064943702766 E - 10, 5.860453293389132 E - 12

1836,45,1.102941176470588,0.027032871972318337,0.0006625703914783906,1.623947037937232E-05,3.9802623478853724E-07,9.755544970307284E-09,2.391064943702766E-10,5.860453293389132E-12

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：

$a_{2} a_{1} = \frac{45}{1836} = 0.024509803921568627$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.024509803921568627$

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： $a = 1, 836$ 、公比： $r = 0.024509803921568627$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1836 * ((1 - {0.024509803921568627}^{2}) / (1 - 0.024509803921568627))$

$s_{2} = 1836 * ((1 - 0.0006007304882737408) / (1 - 0.024509803921568627))$

$s_{2} = 1836 * (0.9993992695117263 / (1 - 0.024509803921568627))$

$s_{2} = 1836 * (0.9993992695117263 / 0.9754901960784313)$

$s_{2} = 1836 \cdot 1.0245098039215688$

$s_{2} = 1881.0000000000002$

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： $a = 1, 836$ 和公比： $r = 0.024509803921568627$ 插入几何级数的公式：

$a_{n} = 1836 \cdot {0.024509803921568627}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1836$

$a_{2} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{2 - 1} = 1836 \cdot {0.024509803921568627}^{1} = 1836 \cdot 0.024509803921568627 = 45$

$a_{3} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{3 - 1} = 1836 \cdot {0.024509803921568627}^{2} = 1836 \cdot 0.0006007304882737408 = 1.102941176470588$

$a_{4} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{4 - 1} = 1836 \cdot {0.024509803921568627}^{3} = 1836 \cdot 1.472378647729757 E - 05 = 0.027032871972318337$

$a_{5} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{5 - 1} = 1836 \cdot {0.024509803921568627}^{4} = 1836 \cdot 3.6087711954160707 E - 07 = 0.0006625703914783906$

$a_{6} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{6 - 1} = 1836 \cdot {0.024509803921568627}^{5} = 1836 \cdot 8.845027439745272 E - 09 = 1.623947037937232 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{7 - 1} = 1836 \cdot {0.024509803921568627}^{6} = 1836 \cdot 2.1678988822905078 E - 10 = 3.9802623478853724 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{8 - 1} = 1836 \cdot {0.024509803921568627}^{7} = 1836 \cdot 5.313477652672813 E - 12 = 9.755544970307284 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{9 - 1} = 1836 \cdot {0.024509803921568627}^{8} = 1836 \cdot 1.3023229540864738 E - 13 = 2.391064943702766 E - 10$

$a_{10} = a_{1} \cdot r^{n - 1} = 1836 \cdot {0.024509803921568627}^{10 - 1} = 1836 \cdot {0.024509803921568627}^{9} = 1836 \cdot 3.1919680247217495 E - 15 = 5.860453293389132 E - 12$

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几何数列