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解答 - 几何数列

公比是：

r = 0.04938271604938271

r=0.04938271604938271

该系列的和是：

s = 85

s=85

此系列的通用形式是：

a_{n} = 81 \cdot {0.04938271604938271}^{n - 1}

a_n=81*0.04938271604938271^(n-1)

这个序列的第n项是：

81, 4, 0.19753086419753083, 0.009754610577655844, 0.0004817091643286836, 2.3788106880428817 E - 05, 1.1747213274285836 E - 06, 5.801092974955968 E - 08, 2.864737271583194 E - 09, 1.4146850723867622 E - 10

81,4,0.19753086419753083,0.009754610577655844,0.0004817091643286836,2.3788106880428817E-05,1.1747213274285836E-06,5.801092974955968E-08,2.864737271583194E-09,1.4146850723867622E-10

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：

$a_{2} a_{1} = \frac{4}{81} = 0.04938271604938271$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.04938271604938271$

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： $a = 81$ 、公比： $r = 0.04938271604938271$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 81 * ((1 - {0.04938271604938271}^{2}) / (1 - 0.04938271604938271))$

$s_{2} = 81 * ((1 - 0.002438652644413961) / (1 - 0.04938271604938271))$

$s_{2} = 81 * (0.997561347355586 / (1 - 0.04938271604938271))$

$s_{2} = 81 * (0.997561347355586 / 0.9506172839506173)$

$s_{2} = 81 \cdot 1.0493827160493827$

$s_{2} = 85$

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： $a = 81$ 和公比： $r = 0.04938271604938271$ 插入几何级数的公式：

$a_{n} = 81 \cdot {0.04938271604938271}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 81$

$a_{2} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{2 - 1} = 81 \cdot {0.04938271604938271}^{1} = 81 \cdot 0.04938271604938271 = 4$

$a_{3} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{3 - 1} = 81 \cdot {0.04938271604938271}^{2} = 81 \cdot 0.002438652644413961 = 0.19753086419753083$

$a_{4} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{4 - 1} = 81 \cdot {0.04938271604938271}^{3} = 81 \cdot 0.0001204272910821709 = 0.009754610577655844$

$a_{5} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{5 - 1} = 81 \cdot {0.04938271604938271}^{4} = 81 \cdot 5.947026720107205 E - 06 = 0.0004817091643286836$

$a_{6} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{6 - 1} = 81 \cdot {0.04938271604938271}^{5} = 81 \cdot 2.936803318571459 E - 07 = 2.3788106880428817 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{7 - 1} = 81 \cdot {0.04938271604938271}^{6} = 81 \cdot 1.450273243738992 E - 08 = 1.1747213274285836 E - 06$

$a_{8} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{8 - 1} = 81 \cdot {0.04938271604938271}^{7} = 81 \cdot 7.161843178957985 E - 10 = 5.801092974955968 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{9 - 1} = 81 \cdot {0.04938271604938271}^{8} = 81 \cdot 3.536712680966906 E - 11 = 2.864737271583194 E - 09$

$a_{10} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.04938271604938271}^{10 - 1} = 81 \cdot {0.04938271604938271}^{9} = 81 \cdot 1.7465247807243979 E - 12 = 1.4146850723867622 E - 10$

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几何数列