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解答 - 几何数列

公比是：

r = 0.22727272727272727

r=0.22727272727272727

该系列的和是：

s = 27

s=27

此系列的通用形式是：

a_{n} = 22 \cdot {0.22727272727272727}^{n - 1}

a_n=22*0.22727272727272727^(n-1)

这个序列的第n项是：

22, 5, 1.1363636363636362, 0.25826446280991733, 0.058696468820435756, 0.013340106550099033, 0.0030318423977497805, 0.0006890550903976775, 0.00015660342963583576, 3.559168855359903 E - 05

22,5,1.1363636363636362,0.25826446280991733,0.058696468820435756,0.013340106550099033,0.0030318423977497805,0.0006890550903976775,0.00015660342963583576,3.559168855359903E-05

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：

$a_{2} a_{1} = \frac{5}{22} = 0.22727272727272727$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.22727272727272727$

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： $r = 0.22727272727272727$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 22 * ((1 - {0.22727272727272727}^{2}) / (1 - 0.22727272727272727))$

$s_{2} = 22 * ((1 - 0.051652892561983466) / (1 - 0.22727272727272727))$

$s_{2} = 22 * (0.9483471074380165 / (1 - 0.22727272727272727))$

$s_{2} = 22 * (0.9483471074380165 / 0.7727272727272727)$

$s_{2} = 22 \cdot 1.2272727272727273$

$s_{2} = 27$

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： $r = 0.22727272727272727$ 插入几何级数的公式：

$a_{n} = 22 \cdot {0.22727272727272727}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 22$

$a_{2} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{2 - 1} = 22 \cdot {0.22727272727272727}^{1} = 22 \cdot 0.22727272727272727 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{3 - 1} = 22 \cdot {0.22727272727272727}^{2} = 22 \cdot 0.051652892561983466 = 1.1363636363636362$

$a_{4} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{4 - 1} = 22 \cdot {0.22727272727272727}^{3} = 22 \cdot 0.01173929376408715 = 0.25826446280991733$

$a_{5} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{5 - 1} = 22 \cdot {0.22727272727272727}^{4} = 22 \cdot 0.002668021310019807 = 0.058696468820435756$

$a_{6} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{6 - 1} = 22 \cdot {0.22727272727272727}^{5} = 22 \cdot 0.0006063684795499561 = 0.013340106550099033$

$a_{7} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{7 - 1} = 22 \cdot {0.22727272727272727}^{6} = 22 \cdot 0.00013781101807953548 = 0.0030318423977497805$

$a_{8} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{8 - 1} = 22 \cdot {0.22727272727272727}^{7} = 22 \cdot 3.1320685927167155 E - 05 = 0.0006890550903976775$

$a_{9} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{9 - 1} = 22 \cdot {0.22727272727272727}^{8} = 22 \cdot 7.118337710719808 E - 06 = 0.00015660342963583576$

$a_{10} = a_{1} \cdot r^{n - 1} = 22 \cdot {0.22727272727272727}^{10 - 1} = 22 \cdot {0.22727272727272727}^{9} = 22 \cdot 1.6178040251635924 E - 06 = 3.559168855359903 E - 05$

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几何数列