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解答 - 几何数列

公比是：

r = 0.015384615384615385

r=0.015384615384615385

该系列的和是：

s = 330

s=330

此系列的通用形式是：

a_{n} = 325 \cdot {0.015384615384615385}^{n - 1}

a_n=325*0.015384615384615385^(n-1)

这个序列的第n项是：

325, 5, 0.07692307692307693, 0.0011834319526627221, 1.820664542558034 E - 05, 2.8010223731662064 E - 07, 4.309265189486472 E - 09, 6.629638753056111 E - 11, 1.0199444235470941 E - 12, 1.5691452669955293 E - 14

325,5,0.07692307692307693,0.0011834319526627221,1.820664542558034E-05,2.8010223731662064E-07,4.309265189486472E-09,6.629638753056111E-11,1.0199444235470941E-12,1.5691452669955293E-14

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：

$a_{2} a_{1} = \frac{5}{325} = 0.015384615384615385$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.015384615384615385$

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： $a = 325$ 、公比： $r = 0.015384615384615385$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 325 * ((1 - {0.015384615384615385}^{2}) / (1 - 0.015384615384615385))$

$s_{2} = 325 * ((1 - 0.0002366863905325444) / (1 - 0.015384615384615385))$

$s_{2} = 325 * (0.9997633136094675 / (1 - 0.015384615384615385))$

$s_{2} = 325 * (0.9997633136094675 / 0.9846153846153847)$

$s_{2} = 325 \cdot 1.0153846153846153$

$s_{2} = 330$

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： $a = 325$ 和公比： $r = 0.015384615384615385$ 插入几何级数的公式：

$a_{n} = 325 \cdot {0.015384615384615385}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 325$

$a_{2} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{2 - 1} = 325 \cdot {0.015384615384615385}^{1} = 325 \cdot 0.015384615384615385 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{3 - 1} = 325 \cdot {0.015384615384615385}^{2} = 325 \cdot 0.0002366863905325444 = 0.07692307692307693$

$a_{4} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{4 - 1} = 325 \cdot {0.015384615384615385}^{3} = 325 \cdot 3.6413290851160678 E - 06 = 0.0011834319526627221$

$a_{5} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{5 - 1} = 325 \cdot {0.015384615384615385}^{4} = 325 \cdot 5.6020447463324125 E - 08 = 1.820664542558034 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{6 - 1} = 325 \cdot {0.015384615384615385}^{5} = 325 \cdot 8.618530378972942 E - 10 = 2.8010223731662064 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{7 - 1} = 325 \cdot {0.015384615384615385}^{6} = 325 \cdot 1.3259277506112221 E - 11 = 4.309265189486472 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{8 - 1} = 325 \cdot {0.015384615384615385}^{7} = 325 \cdot 2.039888847094188 E - 13 = 6.629638753056111 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{9 - 1} = 325 \cdot {0.015384615384615385}^{8} = 325 \cdot 3.1382905339910586 E - 15 = 1.0199444235470941 E - 12$

$a_{10} = a_{1} \cdot r^{n - 1} = 325 \cdot {0.015384615384615385}^{10 - 1} = 325 \cdot {0.015384615384615385}^{9} = 325 \cdot 4.828139283063167 E - 17 = 1.5691452669955293 E - 14$

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几何数列