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解答 - 几何数列

公比是：

r = 0.007082152974504249

r=0.007082152974504249

该系列的和是：

s = 711

s=711

此系列的通用形式是：

a_{n} = 706 \cdot {0.007082152974504249}^{n - 1}

a_n=706*0.007082152974504249^(n-1)

这个序列的第n项是：

706, 5, 0.03541076487252125, 0.0002507844537713969, 1.7760938652365222 E - 06, 1.2578568450683587 E - 08, 8.908334596801406 E - 11, 6.30901883626162 E - 13, 4.468143651743357 E - 15, 3.1644076853706494 E - 17

706,5,0.03541076487252125,0.0002507844537713969,1.7760938652365222E-06,1.2578568450683587E-08,8.908334596801406E-11,6.30901883626162E-13,4.468143651743357E-15,3.1644076853706494E-17

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：

$a_{2} a_{1} = \frac{5}{706} = 0.007082152974504249$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.007082152974504249$

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： $a = 706$ 、公比： $r = 0.007082152974504249$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 706 * ((1 - {0.007082152974504249}^{2}) / (1 - 0.007082152974504249))$

$s_{2} = 706 * ((1 - 5.015689075427939 E - 05) / (1 - 0.007082152974504249))$

$s_{2} = 706 * (0.9999498431092457 / (1 - 0.007082152974504249))$

$s_{2} = 706 * (0.9999498431092457 / 0.9929178470254958)$

$s_{2} = 706 \cdot 1.0070821529745042$

$s_{2} = 711$

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： $a = 706$ 和公比： $r = 0.007082152974504249$ 插入几何级数的公式：

$a_{n} = 706 \cdot {0.007082152974504249}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 706$

$a_{2} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{2 - 1} = 706 \cdot {0.007082152974504249}^{1} = 706 \cdot 0.007082152974504249 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{3 - 1} = 706 \cdot {0.007082152974504249}^{2} = 706 \cdot 5.015689075427939 E - 05 = 0.03541076487252125$

$a_{4} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{4 - 1} = 706 \cdot {0.007082152974504249}^{3} = 706 \cdot 3.5521877304730443 E - 07 = 0.0002507844537713969$

$a_{5} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{5 - 1} = 706 \cdot {0.007082152974504249}^{4} = 706 \cdot 2.515713690136717 E - 09 = 1.7760938652365222 E - 06$

$a_{6} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{6 - 1} = 706 \cdot {0.007082152974504249}^{5} = 706 \cdot 1.7816669193602814 E - 11 = 1.2578568450683587 E - 08$

$a_{7} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{7 - 1} = 706 \cdot {0.007082152974504249}^{6} = 706 \cdot 1.2618037672523238 E - 13 = 8.908334596801406 E - 11$

$a_{8} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{8 - 1} = 706 \cdot {0.007082152974504249}^{7} = 706 \cdot 8.936287303486713 E - 16 = 6.30901883626162 E - 13$

$a_{9} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{9 - 1} = 706 \cdot {0.007082152974504249}^{8} = 706 \cdot 6.328815370741298 E - 18 = 4.468143651743357 E - 15$

$a_{10} = a_{1} \cdot r^{n - 1} = 706 \cdot {0.007082152974504249}^{10 - 1} = 706 \cdot {0.007082152974504249}^{9} = 706 \cdot 4.48216386029837 E - 20 = 3.1644076853706494 E - 17$

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