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解答 - 几何数列

公比是：

r = 0.6363636363636364

r=0.6363636363636364

该系列的和是：

s = 36

s=36

此系列的通用形式是：

a_{n} = 22 \cdot {0.6363636363636364}^{n - 1}

a_n=22*0.6363636363636364^(n-1)

这个序列的第n项是：

22, 14, 8.909090909090908, 5.669421487603305, 3.6078136739293765, 2.2958814288641483, 1.461015454731731, 0.929737107556556, 0.5916508866268992, 0.3765051096716632

22,14,8.909090909090908,5.669421487603305,3.6078136739293765,2.2958814288641483,1.461015454731731,0.929737107556556,0.5916508866268992,0.3765051096716632

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：

$a_{2} a_{1} = \frac{14}{22} = 0.6363636363636364$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.6363636363636364$

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： $a = 22$ 、公比： $r = 0.6363636363636364$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 22 * ((1 - {0.6363636363636364}^{2}) / (1 - 0.6363636363636364))$

$s_{2} = 22 * ((1 - 0.4049586776859504) / (1 - 0.6363636363636364))$

$s_{2} = 22 * (0.5950413223140496 / (1 - 0.6363636363636364))$

$s_{2} = 22 * (0.5950413223140496 / 0.36363636363636365)$

$s_{2} = 22 \cdot 1.6363636363636365$

$s_{2} = 36$

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： $a = 22$ 和公比： $r = 0.6363636363636364$ 插入几何级数的公式：

$a_{n} = 22 \cdot {0.6363636363636364}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 22$

$a_{2} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{2 - 1} = 22 \cdot {0.6363636363636364}^{1} = 22 \cdot 0.6363636363636364 = 14$

$a_{3} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{3 - 1} = 22 \cdot {0.6363636363636364}^{2} = 22 \cdot 0.4049586776859504 = 8.909090909090908$

$a_{4} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{4 - 1} = 22 \cdot {0.6363636363636364}^{3} = 22 \cdot 0.25770097670924114 = 5.669421487603305$

$a_{5} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{5 - 1} = 22 \cdot {0.6363636363636364}^{4} = 22 \cdot 0.16399153063315347 = 3.6078136739293765$

$a_{6} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{6 - 1} = 22 \cdot {0.6363636363636364}^{5} = 22 \cdot 0.1043582467665522 = 2.2958814288641483$

$a_{7} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{7 - 1} = 22 \cdot {0.6363636363636364}^{6} = 22 \cdot 0.06640979339689686 = 1.461015454731731$

$a_{8} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{8 - 1} = 22 \cdot {0.6363636363636364}^{7} = 22 \cdot 0.04226077761620709 = 0.929737107556556$

$a_{9} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{9 - 1} = 22 \cdot {0.6363636363636364}^{8} = 22 \cdot 0.026893222119404512 = 0.5916508866268992$

$a_{10} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.6363636363636364}^{10 - 1} = 22 \cdot {0.6363636363636364}^{9} = 22 \cdot 0.017113868621439234 = 0.3765051096716632$

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