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解答 - 几何数列

公比是：

r = 0.1509433962264151

r=0.1509433962264151

该系列的和是：

s = 61

s=61

此系列的通用形式是：

a_{n} = 53 \cdot {0.1509433962264151}^{n - 1}

a_n=53*0.1509433962264151^(n-1)

这个序列的第n项是：

53, 8, 1.2075471698113207, 0.18227127091491632, 0.027512644666402464, 0.004152852025117353, 0.0006268455886969588, 9.461820206746548 E - 05, 1.4281992764900451 E - 05, 2.1557724928151624 E - 06

53,8,1.2075471698113207,0.18227127091491632,0.027512644666402464,0.004152852025117353,0.0006268455886969588,9.461820206746548E-05,1.4281992764900451E-05,2.1557724928151624E-06

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：

$a_{2} a_{1} = \frac{8}{53} = 0.1509433962264151$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.1509433962264151$

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： $a = 53$ 、公比： $r = 0.1509433962264151$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 53 * ((1 - {0.1509433962264151}^{2}) / (1 - 0.1509433962264151))$

$s_{2} = 53 * ((1 - 0.02278390886436454) / (1 - 0.1509433962264151))$

$s_{2} = 53 * (0.9772160911356355 / (1 - 0.1509433962264151))$

$s_{2} = 53 * (0.9772160911356355 / 0.8490566037735849)$

$s_{2} = 53 \cdot 1.150943396226415$

$s_{2} = 61$

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： $a = 53$ 和公比： $r = 0.1509433962264151$ 插入几何级数的公式：

$a_{n} = 53 \cdot {0.1509433962264151}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 53$

$a_{2} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{2 - 1} = 53 \cdot {0.1509433962264151}^{1} = 53 \cdot 0.1509433962264151 = 8$

$a_{3} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{3 - 1} = 53 \cdot {0.1509433962264151}^{2} = 53 \cdot 0.02278390886436454 = 1.2075471698113207$

$a_{4} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{4 - 1} = 53 \cdot {0.1509433962264151}^{3} = 53 \cdot 0.003439080583300308 = 0.18227127091491632$

$a_{5} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{5 - 1} = 53 \cdot {0.1509433962264151}^{4} = 53 \cdot 0.0005191065031396691 = 0.027512644666402464$

$a_{6} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{6 - 1} = 53 \cdot {0.1509433962264151}^{5} = 53 \cdot 7.835569858711986 E - 05 = 0.004152852025117353$

$a_{7} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{7 - 1} = 53 \cdot {0.1509433962264151}^{6} = 53 \cdot 1.1827275258433185 E - 05 = 0.0006268455886969588$

$a_{8} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{8 - 1} = 53 \cdot {0.1509433962264151}^{7} = 53 \cdot 1.7852490956125564 E - 06 = 9.461820206746548 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{9 - 1} = 53 \cdot {0.1509433962264151}^{8} = 53 \cdot 2.694715616018953 E - 07 = 1.4281992764900451 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.1509433962264151}^{10 - 1} = 53 \cdot {0.1509433962264151}^{9} = 53 \cdot 4.0674952694625703 E - 08 = 2.1557724928151624 E - 06$

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几何数列