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解答 - 几何数列

公比是：

r = 0.21052631578947367

r=0.21052631578947367

该系列的和是：

s = 69

s=69

此系列的通用形式是：

a_{n} = 57 \cdot {0.21052631578947367}^{n - 1}

a_n=57*0.21052631578947367^(n-1)

这个序列的第n项是：

57, 12, 2.5263157894736836, 0.5318559556786703, 0.11196967487972005, 0.02357256313257264, 0.004962644870015293, 0.0010447673410558511, 0.00021995101916965284, 4.630547771992691 E - 05

57,12,2.5263157894736836,0.5318559556786703,0.11196967487972005,0.02357256313257264,0.004962644870015293,0.0010447673410558511,0.00021995101916965284,4.630547771992691E-05

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：

$a_{2} a_{1} = \frac{12}{57} = 0.21052631578947367$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.21052631578947367$

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： $a = 57$ 、公比： $r = 0.21052631578947367$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 57 * ((1 - {0.21052631578947367}^{2}) / (1 - 0.21052631578947367))$

$s_{2} = 57 * ((1 - 0.04432132963988919) / (1 - 0.21052631578947367))$

$s_{2} = 57 * (0.9556786703601108 / (1 - 0.21052631578947367))$

$s_{2} = 57 * (0.9556786703601108 / 0.7894736842105263)$

$s_{2} = 57 \cdot 1.2105263157894737$

$s_{2} = 69$

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： $a = 57$ 和公比： $r = 0.21052631578947367$ 插入几何级数的公式：

$a_{n} = 57 \cdot {0.21052631578947367}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 57$

$a_{2} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{2 - 1} = 57 \cdot {0.21052631578947367}^{1} = 57 \cdot 0.21052631578947367 = 12$

$a_{3} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{3 - 1} = 57 \cdot {0.21052631578947367}^{2} = 57 \cdot 0.04432132963988919 = 2.5263157894736836$

$a_{4} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{4 - 1} = 57 \cdot {0.21052631578947367}^{3} = 57 \cdot 0.009330806239976671 = 0.5318559556786703$

$a_{5} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{5 - 1} = 57 \cdot {0.21052631578947367}^{4} = 57 \cdot 0.0019643802610477203 = 0.11196967487972005$

$a_{6} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{6 - 1} = 57 \cdot {0.21052631578947367}^{5} = 57 \cdot 0.0004135537391679411 = 0.02357256313257264$

$a_{7} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{7 - 1} = 57 \cdot {0.21052631578947367}^{6} = 57 \cdot 8.70639450879876 E - 05 = 0.004962644870015293$

$a_{8} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{8 - 1} = 57 \cdot {0.21052631578947367}^{7} = 57 \cdot 1.832925159747107 E - 05 = 0.0010447673410558511$

$a_{9} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{9 - 1} = 57 \cdot {0.21052631578947367}^{8} = 57 \cdot 3.858789809993909 E - 06 = 0.00021995101916965284$

$a_{10} = a_{1} \cdot r^{n - 1} = 57 \cdot {0.21052631578947367}^{10 - 1} = 57 \cdot {0.21052631578947367}^{9} = 57 \cdot 8.123768021039809 E - 07 = 4.630547771992691 E - 05$

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几何数列