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解答 - 几何数列

公比是：

r = 0.014084507042253521

r=0.014084507042253521

该系列的和是：

s = 360

s=360

此系列的通用形式是：

a_{n} = 355 \cdot {0.014084507042253521}^{n - 1}

a_n=355*0.014084507042253521^(n-1)

这个序列的第n项是：

355, 5, 0.07042253521126761, 0.0009918666931164452, 1.3969953424175284 E - 05, 1.967599073827505 E - 07, 2.7712663011654997 E - 09, 3.903191973472536 E - 11, 5.497453483764135 E - 13, 7.74289223065371 E - 15

355,5,0.07042253521126761,0.0009918666931164452,1.3969953424175284E-05,1.967599073827505E-07,2.7712663011654997E-09,3.903191973472536E-11,5.497453483764135E-13,7.74289223065371E-15

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：

$a_{2} a_{1} = \frac{5}{355} = 0.014084507042253521$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.014084507042253521$

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： $a = 355$ 、公比： $r = 0.014084507042253521$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 355 * ((1 - {0.014084507042253521}^{2}) / (1 - 0.014084507042253521))$

$s_{2} = 355 * ((1 - 0.00019837333862328903) / (1 - 0.014084507042253521))$

$s_{2} = 355 * (0.9998016266613767 / (1 - 0.014084507042253521))$

$s_{2} = 355 * (0.9998016266613767 / 0.9859154929577465)$

$s_{2} = 355 \cdot 1.0140845070422535$

$s_{2} = 360$

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： $a = 355$ 和公比： $r = 0.014084507042253521$ 插入几何级数的公式：

$a_{n} = 355 \cdot {0.014084507042253521}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 355$

$a_{2} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{2 - 1} = 355 \cdot {0.014084507042253521}^{1} = 355 \cdot 0.014084507042253521 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{3 - 1} = 355 \cdot {0.014084507042253521}^{2} = 355 \cdot 0.00019837333862328903 = 0.07042253521126761$

$a_{4} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{4 - 1} = 355 \cdot {0.014084507042253521}^{3} = 355 \cdot 2.793990684835057 E - 06 = 0.0009918666931164452$

$a_{5} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{5 - 1} = 355 \cdot {0.014084507042253521}^{4} = 355 \cdot 3.93519814765501 E - 08 = 1.3969953424175284 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{6 - 1} = 355 \cdot {0.014084507042253521}^{5} = 355 \cdot 5.542532602331 E - 10 = 1.967599073827505 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{7 - 1} = 355 \cdot {0.014084507042253521}^{6} = 355 \cdot 7.80638394694507 E - 12 = 2.7712663011654997 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{8 - 1} = 355 \cdot {0.014084507042253521}^{7} = 355 \cdot 1.0994906967528269 E - 13 = 3.903191973472536 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{9 - 1} = 355 \cdot {0.014084507042253521}^{8} = 355 \cdot 1.548578446130742 E - 15 = 5.497453483764135 E - 13$

$a_{10} = a_{1} \cdot r^{n - 1} = 355 \cdot {0.014084507042253521}^{10 - 1} = 355 \cdot {0.014084507042253521}^{9} = 355 \cdot 2.1810964030010452 E - 17 = 7.74289223065371 E - 15$

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几何数列