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解答 - 几何数列

公比是：

r = 23.846153846153847

r=23.846153846153847

该系列的和是：

s = 645

s=645

此系列的通用形式是：

a_{n} = 26 \cdot {23.846153846153847}^{n - 1}

a_n=26*23.846153846153847^(n-1)

这个序列的第n项是：

26, 620, 14784.615384615383, 352556.2130177515, 8407109.69503869, 200477231.18938413, 4780610897.593007, 113999182942.60246, 2718442054785.1357, 64824387460260.94

26,620,14784.615384615383,352556.2130177515,8407109.69503869,200477231.18938413,4780610897.593007,113999182942.60246,2718442054785.1357,64824387460260.94

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：

$a_{2} a_{1} = \frac{620}{26} = 23.846153846153847$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 23.846153846153847$

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： $a = 26$ 、公比： $r = 23.846153846153847$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 26 * ((1 - {23.846153846153847}^{2}) / (1 - 23.846153846153847))$

$s_{2} = 26 * ((1 - 568.6390532544378) / (1 - 23.846153846153847))$

$s_{2} = 26 * (- 567.6390532544378 / (1 - 23.846153846153847))$

$s_{2} = 26 * (- 567.6390532544378 / - 22.846153846153847)$

$s_{2} = 26 \cdot 24.846153846153843$

$s_{2} = 645.9999999999999$

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： $a = 26$ 和公比： $r = 23.846153846153847$ 插入几何级数的公式：

$a_{n} = 26 \cdot {23.846153846153847}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 26$

$a_{2} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{2 - 1} = 26 \cdot {23.846153846153847}^{1} = 26 \cdot 23.846153846153847 = 620$

$a_{3} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{3 - 1} = 26 \cdot {23.846153846153847}^{2} = 26 \cdot 568.6390532544378 = 14784.615384615383$

$a_{4} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{4 - 1} = 26 \cdot {23.846153846153847}^{3} = 26 \cdot 13559.854346836597 = 352556.2130177515$

$a_{5} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{5 - 1} = 26 \cdot {23.846153846153847}^{4} = 26 \cdot 323350.37288610346 = 8407109.69503869$

$a_{6} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{6 - 1} = 26 \cdot {23.846153846153847}^{5} = 26 \cdot 7710662.738053236 = 200477231.18938413$

$a_{7} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{7 - 1} = 26 \cdot {23.846153846153847}^{6} = 26 \cdot 183869649.90742335 = 4780610897.593007$

$a_{8} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{8 - 1} = 26 \cdot {23.846153846153847}^{7} = 26 \cdot 4384583959.330864 = 113999182942.60246$

$a_{9} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{9 - 1} = 26 \cdot {23.846153846153847}^{8} = 26 \cdot 104555463645.58215 = 2718442054785.1357$

$a_{10} = a_{1} \cdot r^{n - 1} = 26 \cdot {23.846153846153847}^{10 - 1} = 26 \cdot {23.846153846153847}^{9} = 26 \cdot 2493245671548.4976 = 64824387460260.94$

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