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解答 - 几何数列

公比是：

r = 0.28994082840236685

r=0.28994082840236685

该系列的和是：

s = 218

s=218

此系列的通用形式是：

a_{n} = 169 \cdot {0.28994082840236685}^{n - 1}

a_n=169*0.28994082840236685^(n-1)

这个序列的第n项是：

169, 49, 14.207100591715975, 4.119218514757886, 1.1943296285392686, 0.3462849218841666, 0.10040213711434416, 0.02911067880830097, 0.008440374329034007, 0.0024472091249861916

169,49,14.207100591715975,4.119218514757886,1.1943296285392686,0.3462849218841666,0.10040213711434416,0.02911067880830097,0.008440374329034007,0.0024472091249861916

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：

$a_{2} a_{1} = \frac{49}{169} = 0.28994082840236685$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.28994082840236685$

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： $a = 169$ 、公比： $r = 0.28994082840236685$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 169 * ((1 - {0.28994082840236685}^{2}) / (1 - 0.28994082840236685))$

$s_{2} = 169 * ((1 - 0.08406568397465074) / (1 - 0.28994082840236685))$

$s_{2} = 169 * (0.9159343160253492 / (1 - 0.28994082840236685))$

$s_{2} = 169 * (0.9159343160253492 / 0.7100591715976332)$

$s_{2} = 169 \cdot 1.2899408284023668$

$s_{2} = 218$

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： $a = 169$ 和公比： $r = 0.28994082840236685$ 插入几何级数的公式：

$a_{n} = 169 \cdot {0.28994082840236685}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 169$

$a_{2} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{2 - 1} = 169 \cdot {0.28994082840236685}^{1} = 169 \cdot 0.28994082840236685 = 49$

$a_{3} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{3 - 1} = 169 \cdot {0.28994082840236685}^{2} = 169 \cdot 0.08406568397465074 = 14.207100591715975$

$a_{4} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{4 - 1} = 169 \cdot {0.28994082840236685}^{3} = 169 \cdot 0.02437407405182181 = 4.119218514757886$

$a_{5} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{5 - 1} = 169 \cdot {0.28994082840236685}^{4} = 169 \cdot 0.00706703922212585 = 1.1943296285392686$

$a_{6} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{6 - 1} = 169 \cdot {0.28994082840236685}^{5} = 169 \cdot 0.002049023206415187 = 0.3462849218841666$

$a_{7} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{7 - 1} = 169 \cdot {0.28994082840236685}^{6} = 169 \cdot 0.0005940954858836933 = 0.10040213711434416$

$a_{8} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{8 - 1} = 169 \cdot {0.28994082840236685}^{7} = 169 \cdot 0.00017225253732722467 = 0.02911067880830097$

$a_{9} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{9 - 1} = 169 \cdot {0.28994082840236685}^{8} = 169 \cdot 4.994304336706513 E - 05 = 0.008440374329034007$

$a_{10} = a_{1} \cdot r^{n - 1} = 169 \cdot {0.28994082840236685}^{10 - 1} = 169 \cdot {0.28994082840236685}^{9} = 169 \cdot 1.4480527366782199 E - 05 = 0.0024472091249861916$

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几何数列