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解答 - 几何数列

公比是：

r = 0.08791208791208792

r=0.08791208791208792

该系列的和是：

s = 99

s=99

此系列的通用形式是：

a_{n} = 91 \cdot {0.08791208791208792}^{n - 1}

a_n=91*0.08791208791208792^(n-1)

这个序列的第n项是：

91, 8, 0.7032967032967035, 0.0618282816085014, 0.005435453328219904, 0.0004778420508325191, 4.20080923808808 E - 05, 3.6930191104071032 E - 06, 3.2466102069513 E - 07, 2.8541628192978466 E - 08

91,8,0.7032967032967035,0.0618282816085014,0.005435453328219904,0.0004778420508325191,4.20080923808808E-05,3.6930191104071032E-06,3.2466102069513E-07,2.8541628192978466E-08

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：

$a_{2} a_{1} = \frac{8}{91} = 0.08791208791208792$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.08791208791208792$

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： $a = 91$ 、公比： $r = 0.08791208791208792$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 91 * ((1 - {0.08791208791208792}^{2}) / (1 - 0.08791208791208792))$

$s_{2} = 91 * ((1 - 0.007728535201062675) / (1 - 0.08791208791208792))$

$s_{2} = 91 * (0.9922714647989374 / (1 - 0.08791208791208792))$

$s_{2} = 91 * (0.9922714647989374 / 0.9120879120879121)$

$s_{2} = 91 \cdot 1.087912087912088$

$s_{2} = 99.00000000000001$

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： $a = 91$ 和公比： $r = 0.08791208791208792$ 插入几何级数的公式：

$a_{n} = 91 \cdot {0.08791208791208792}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 91$

$a_{2} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{2 - 1} = 91 \cdot {0.08791208791208792}^{1} = 91 \cdot 0.08791208791208792 = 8$

$a_{3} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{3 - 1} = 91 \cdot {0.08791208791208792}^{2} = 91 \cdot 0.007728535201062675 = 0.7032967032967035$

$a_{4} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{4 - 1} = 91 \cdot {0.08791208791208792}^{3} = 91 \cdot 0.0006794316660274879 = 0.0618282816085014$

$a_{5} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{5 - 1} = 91 \cdot {0.08791208791208792}^{4} = 91 \cdot 5.973025635406488 E - 05 = 0.005435453328219904$

$a_{6} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{6 - 1} = 91 \cdot {0.08791208791208792}^{5} = 91 \cdot 5.2510115476101 E - 06 = 0.0004778420508325191$

$a_{7} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{7 - 1} = 91 \cdot {0.08791208791208792}^{6} = 91 \cdot 4.616273888008879 E - 07 = 4.20080923808808 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{8 - 1} = 91 \cdot {0.08791208791208792}^{7} = 91 \cdot 4.0582627586891246 E - 08 = 3.6930191104071032 E - 06$

$a_{9} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{9 - 1} = 91 \cdot {0.08791208791208792}^{8} = 91 \cdot 3.567703524122308 E - 09 = 3.2466102069513 E - 07$

$a_{10} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.08791208791208792}^{10 - 1} = 91 \cdot {0.08791208791208792}^{9} = 91 \cdot 3.136442658569062 E - 10 = 2.8541628192978466 E - 08$

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几何数列