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解答 - 几何数列

公比是：

r = 0.34210526315789475

r=0.34210526315789475

该系列的和是：

s = 50

s=50

此系列的通用形式是：

a_{n} = 38 \cdot {0.34210526315789475}^{n - 1}

a_n=38*0.34210526315789475^(n-1)

这个序列的第n项是：

38, 13, 4.447368421052632, 1.5214681440443214, 0.5205022598046363, 0.178066562564744, 0.060917508245833474, 0.020840200189364083, 0.007129542170045608, 0.002439053900278761

38,13,4.447368421052632,1.5214681440443214,0.5205022598046363,0.178066562564744,0.060917508245833474,0.020840200189364083,0.007129542170045608,0.002439053900278761

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：

$a_{2} a_{1} = \frac{13}{38} = 0.34210526315789475$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.34210526315789475$

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： $a = 38$ 、公比： $r = 0.34210526315789475$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 38 * ((1 - {0.34210526315789475}^{2}) / (1 - 0.34210526315789475))$

$s_{2} = 38 * ((1 - 0.11703601108033242) / (1 - 0.34210526315789475))$

$s_{2} = 38 * (0.8829639889196675 / (1 - 0.34210526315789475))$

$s_{2} = 38 * (0.8829639889196675 / 0.6578947368421053)$

$s_{2} = 38 \cdot 1.3421052631578945$

$s_{2} = 50.99999999999999$

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： $a = 38$ 和公比： $r = 0.34210526315789475$ 插入几何级数的公式：

$a_{n} = 38 \cdot {0.34210526315789475}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 38$

$a_{2} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{2 - 1} = 38 \cdot {0.34210526315789475}^{1} = 38 \cdot 0.34210526315789475 = 13$

$a_{3} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{3 - 1} = 38 \cdot {0.34210526315789475}^{2} = 38 \cdot 0.11703601108033242 = 4.447368421052632$

$a_{4} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{4 - 1} = 38 \cdot {0.34210526315789475}^{3} = 38 \cdot 0.040038635369587405 = 1.5214681440443214$

$a_{5} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{5 - 1} = 38 \cdot {0.34210526315789475}^{4} = 38 \cdot 0.013697427889595692 = 0.5205022598046363$

$a_{6} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{6 - 1} = 38 \cdot {0.34210526315789475}^{5} = 38 \cdot 0.004685962172756421 = 0.178066562564744$

$a_{7} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{7 - 1} = 38 \cdot {0.34210526315789475}^{6} = 38 \cdot 0.0016030923222587756 = 0.060917508245833474$

$a_{8} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{8 - 1} = 38 \cdot {0.34210526315789475}^{7} = 38 \cdot 0.0005484263207727391 = 0.020840200189364083$

$a_{9} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{9 - 1} = 38 \cdot {0.34210526315789475}^{8} = 38 \cdot 0.0001876195307906739 = 0.007129542170045608$

$a_{10} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.34210526315789475}^{10 - 1} = 38 \cdot {0.34210526315789475}^{9} = 38 \cdot 6.418562895470423 E - 05 = 0.002439053900278761$

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几何数列