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解答 - 几何数列

公比是：

r = 0.038461538461538464

r=0.038461538461538464

该系列的和是：

s = 27

s=27

此系列的通用形式是：

a_{n} = 26 \cdot {0.038461538461538464}^{n - 1}

a_n=26*0.038461538461538464^(n-1)

这个序列的第n项是：

26, 1, 0.038461538461538464, 0.0014792899408284025, 5.689576695493857 E - 05, 2.1882987290360987 E - 06, 8.416533573215765 E - 08, 3.2371282973906793 E - 09, 1.2450493451502612 E - 10, 4.7886513275010046 E - 12

26,1,0.038461538461538464,0.0014792899408284025,5.689576695493857E-05,2.1882987290360987E-06,8.416533573215765E-08,3.2371282973906793E-09,1.2450493451502612E-10,4.7886513275010046E-12

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：

$a_{2} a_{1} = \frac{1}{26} = 0.038461538461538464$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.038461538461538464$

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： $a = 26$ 、公比： $r = 0.038461538461538464$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 26 * ((1 - {0.038461538461538464}^{2}) / (1 - 0.038461538461538464))$

$s_{2} = 26 * ((1 - 0.0014792899408284025) / (1 - 0.038461538461538464))$

$s_{2} = 26 * (0.9985207100591716 / (1 - 0.038461538461538464))$

$s_{2} = 26 * (0.9985207100591716 / 0.9615384615384616)$

$s_{2} = 26 \cdot 1.0384615384615385$

$s_{2} = 27.000000000000004$

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： $a = 26$ 和公比： $r = 0.038461538461538464$ 插入几何级数的公式：

$a_{n} = 26 \cdot {0.038461538461538464}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 26$

$a_{2} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{2 - 1} = 26 \cdot {0.038461538461538464}^{1} = 26 \cdot 0.038461538461538464 = 1$

$a_{3} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{3 - 1} = 26 \cdot {0.038461538461538464}^{2} = 26 \cdot 0.0014792899408284025 = 0.038461538461538464$

$a_{4} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{4 - 1} = 26 \cdot {0.038461538461538464}^{3} = 26 \cdot 5.689576695493856 E - 05 = 0.0014792899408284025$

$a_{5} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{5 - 1} = 26 \cdot {0.038461538461538464}^{4} = 26 \cdot 2.1882987290360987 E - 06 = 5.689576695493857 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{6 - 1} = 26 \cdot {0.038461538461538464}^{5} = 26 \cdot 8.416533573215765 E - 08 = 2.1882987290360987 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{7 - 1} = 26 \cdot {0.038461538461538464}^{6} = 26 \cdot 3.237128297390679 E - 09 = 8.416533573215765 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{8 - 1} = 26 \cdot {0.038461538461538464}^{7} = 26 \cdot 1.2450493451502612 E - 10 = 3.2371282973906793 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{9 - 1} = 26 \cdot {0.038461538461538464}^{8} = 26 \cdot 4.7886513275010046 E - 12 = 1.2450493451502612 E - 10$

$a_{10} = a_{1} \cdot r^{n - 1} = 26 \cdot {0.038461538461538464}^{10 - 1} = 26 \cdot {0.038461538461538464}^{9} = 26 \cdot 1.841788972115771 E - 13 = 4.7886513275010046 E - 12$

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几何数列