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解答 - 几何数列

公比是：

r = 1.3846153846153846

r=1.3846153846153846

该系列的和是：

s = 61

s=61

此系列的通用形式是：

a_{n} = 26 \cdot {1.3846153846153846}^{n - 1}

a_n=26*1.3846153846153846^(n-1)

这个序列的第n项是：

26, 36, 49.84615384615384, 69.01775147928993, 95.56304050978606, 132.31805609047302, 183.20961612527032, 253.6748530965281, 351.24210428750047, 486.3352213211545

26,36,49.84615384615384,69.01775147928993,95.56304050978606,132.31805609047302,183.20961612527032,253.6748530965281,351.24210428750047,486.3352213211545

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：

$a_{2} a_{1} = \frac{36}{26} = 1.3846153846153846$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.3846153846153846$

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： $r = 1.3846153846153846$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 26 * ((1 - {1.3846153846153846}^{2}) / (1 - 1.3846153846153846))$

$s_{2} = 26 * ((1 - 1.9171597633136093) / (1 - 1.3846153846153846))$

$s_{2} = 26 * (- 0.9171597633136093 / (1 - 1.3846153846153846))$

$s_{2} = 26 * (- 0.9171597633136093 / - 0.3846153846153846)$

$s_{2} = 26 \cdot 2.384615384615384$

$s_{2} = 61.999999999999986$

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： $r = 1.3846153846153846$ 插入几何级数的公式：

$a_{n} = 26 \cdot {1.3846153846153846}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 26$

$a_{2} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{2 - 1} = 26 \cdot {1.3846153846153846}^{1} = 26 \cdot 1.3846153846153846 = 36$

$a_{3} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{3 - 1} = 26 \cdot {1.3846153846153846}^{2} = 26 \cdot 1.9171597633136093 = 49.84615384615384$

$a_{4} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{4 - 1} = 26 \cdot {1.3846153846153846}^{3} = 26 \cdot 2.654528903049613 = 69.01775147928993$

$a_{5} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{5 - 1} = 26 \cdot {1.3846153846153846}^{4} = 26 \cdot 3.6755015580686945 = 95.56304050978606$

$a_{6} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{6 - 1} = 26 \cdot {1.3846153846153846}^{5} = 26 \cdot 5.089156003479731 = 132.31805609047302$

$a_{7} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{7 - 1} = 26 \cdot {1.3846153846153846}^{6} = 26 \cdot 7.046523697125782 = 183.20961612527032$

$a_{8} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{8 - 1} = 26 \cdot {1.3846153846153846}^{7} = 26 \cdot 9.756725119097235 = 253.6748530965281$

$a_{9} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{9 - 1} = 26 \cdot {1.3846153846153846}^{8} = 26 \cdot 13.509311703365402 = 351.24210428750047$

$a_{10} = a_{1} \cdot r^{n - 1} = 26 \cdot {1.3846153846153846}^{10 - 1} = 26 \cdot {1.3846153846153846}^{9} = 26 \cdot 18.705200820044404 = 486.3352213211545$

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