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解答 - 几何数列

公比是：

r = 0.0013713658804168952

r=0.0013713658804168952

该系列的和是：

s = 3651

s=3651

此系列的通用形式是：

a_{n} = 3646 \cdot {0.0013713658804168952}^{n - 1}

a_n=3646*0.0013713658804168952^(n-1)

这个序列的第n项是：

3646, 5, 0.006856829402084477, 9.403221889858031 E - 06, 1.289525766574058 E - 08, 1.768411638198105 E - 11, 2.425139383157028 E - 14, 3.325753405316824 E - 17, 4.560824746731794 E - 20, 6.25455944422901 E - 23

3646,5,0.006856829402084477,9.403221889858031E-06,1.289525766574058E-08,1.768411638198105E-11,2.425139383157028E-14,3.325753405316824E-17,4.560824746731794E-20,6.25455944422901E-23

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：

$a_{2} a_{1} = \frac{5}{3646} = 0.0013713658804168952$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0013713658804168952$

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： $a = 3, 646$ 、公比： $r = 0.0013713658804168952$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 3646 * ((1 - {0.0013713658804168952}^{2}) / (1 - 0.0013713658804168952))$

$s_{2} = 3646 * ((1 - 1.8806443779716063 E - 06) / (1 - 0.0013713658804168952))$

$s_{2} = 3646 * (0.999998119355622 / (1 - 0.0013713658804168952))$

$s_{2} = 3646 * (0.999998119355622 / 0.9986286341195831)$

$s_{2} = 3646 \cdot 1.0013713658804169$

$s_{2} = 3651$

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： $a = 3, 646$ 和公比： $r = 0.0013713658804168952$ 插入几何级数的公式：

$a_{n} = 3646 \cdot {0.0013713658804168952}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 3646$

$a_{2} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{2 - 1} = 3646 \cdot {0.0013713658804168952}^{1} = 3646 \cdot 0.0013713658804168952 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{3 - 1} = 3646 \cdot {0.0013713658804168952}^{2} = 3646 \cdot 1.8806443779716063 E - 06 = 0.006856829402084477$

$a_{4} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{4 - 1} = 3646 \cdot {0.0013713658804168952}^{3} = 3646 \cdot 2.579051533148116 E - 09 = 9.403221889858031 E - 06$

$a_{5} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{5 - 1} = 3646 \cdot {0.0013713658804168952}^{4} = 3646 \cdot 3.5368232763962095 E - 12 = 1.289525766574058 E - 08$

$a_{6} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{6 - 1} = 3646 \cdot {0.0013713658804168952}^{5} = 3646 \cdot 4.850278766314056 E - 15 = 1.768411638198105 E - 11$

$a_{7} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{7 - 1} = 3646 \cdot {0.0013713658804168952}^{6} = 3646 \cdot 6.651506810633648 E - 18 = 2.425139383157028 E - 14$

$a_{8} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{8 - 1} = 3646 \cdot {0.0013713658804168952}^{7} = 3646 \cdot 9.121649493463588 E - 21 = 3.325753405316824 E - 17$

$a_{9} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{9 - 1} = 3646 \cdot {0.0013713658804168952}^{8} = 3646 \cdot 1.2509118888458019 E - 23 = 4.560824746731794 E - 20$

$a_{10} = a_{1} \cdot r^{n - 1} = 3646 \cdot {0.0013713658804168952}^{10 - 1} = 3646 \cdot {0.0013713658804168952}^{9} = 3646 \cdot 1.7154578837709846 E - 26 = 6.25455944422901 E - 23$

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几何数列