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解答 - 几何数列

公比是：

r = 0.3684210526315789

r=0.3684210526315789

该系列的和是：

s = 104

s=104

此系列的通用形式是：

a_{n} = 76 \cdot {0.3684210526315789}^{n - 1}

a_n=76*0.3684210526315789^(n-1)

这个序列的第n项是：

76, 28, 10.315789473684209, 3.800554016620498, 1.4002041113864991, 0.5158646726160786, 0.19005540570066054, 0.07002041262655914, 0.02579699412557442, 0.009504155730474785

76,28,10.315789473684209,3.800554016620498,1.4002041113864991,0.5158646726160786,0.19005540570066054,0.07002041262655914,0.02579699412557442,0.009504155730474785

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：

$a_{2} a_{1} = \frac{28}{76} = 0.3684210526315789$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.3684210526315789$

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： $a = 76$ 、公比： $r = 0.3684210526315789$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 76 * ((1 - {0.3684210526315789}^{2}) / (1 - 0.3684210526315789))$

$s_{2} = 76 * ((1 - 0.13573407202216065) / (1 - 0.3684210526315789))$

$s_{2} = 76 * (0.8642659279778393 / (1 - 0.3684210526315789))$

$s_{2} = 76 * (0.8642659279778393 / 0.631578947368421)$

$s_{2} = 76 \cdot 1.368421052631579$

$s_{2} = 104$

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： $a = 76$ 和公比： $r = 0.3684210526315789$ 插入几何级数的公式：

$a_{n} = 76 \cdot {0.3684210526315789}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 76$

$a_{2} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{2 - 1} = 76 \cdot {0.3684210526315789}^{1} = 76 \cdot 0.3684210526315789 = 28$

$a_{3} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{3 - 1} = 76 \cdot {0.3684210526315789}^{2} = 76 \cdot 0.13573407202216065 = 10.315789473684209$

$a_{4} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{4 - 1} = 76 \cdot {0.3684210526315789}^{3} = 76 \cdot 0.05000728969237497 = 3.800554016620498$

$a_{5} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{5 - 1} = 76 \cdot {0.3684210526315789}^{4} = 76 \cdot 0.018423738307717093 = 1.4002041113864991$

$a_{6} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{6 - 1} = 76 \cdot {0.3684210526315789}^{5} = 76 \cdot 0.0067876930607378766 = 0.5158646726160786$

$a_{7} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{7 - 1} = 76 \cdot {0.3684210526315789}^{6} = 76 \cdot 0.0025007290223771125 = 0.19005540570066054$

$a_{8} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{8 - 1} = 76 \cdot {0.3684210526315789}^{7} = 76 \cdot 0.000921321218770515 = 0.07002041262655914$

$a_{9} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{9 - 1} = 76 \cdot {0.3684210526315789}^{8} = 76 \cdot 0.00033943413323124234 = 0.02579699412557442$

$a_{10} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.3684210526315789}^{10 - 1} = 76 \cdot {0.3684210526315789}^{9} = 76 \cdot 0.0001250546806641419 = 0.009504155730474785$

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