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解答 - 几何数列

公比是：

r = 0.18867924528301888

r=0.18867924528301888

该系列的和是：

s = 63

s=63

此系列的通用形式是：

a_{n} = 53 \cdot {0.18867924528301888}^{n - 1}

a_n=53*0.18867924528301888^(n-1)

这个序列的第n项是：

53, 10, 1.8867924528301887, 0.35599857600569607, 0.06716954264258417, 0.012673498611808335, 0.0023912261531713838, 0.00045117474588139326, 8.51273105436591 E - 05, 1.606175670635078 E - 05

53,10,1.8867924528301887,0.35599857600569607,0.06716954264258417,0.012673498611808335,0.0023912261531713838,0.00045117474588139326,8.51273105436591E-05,1.606175670635078E-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：

$a_{2} a_{1} = \frac{10}{53} = 0.18867924528301888$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.18867924528301888$

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： $r = 0.18867924528301888$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 53 * ((1 - {0.18867924528301888}^{2}) / (1 - 0.18867924528301888))$

$s_{2} = 53 * ((1 - 0.0355998576005696) / (1 - 0.18867924528301888))$

$s_{2} = 53 * (0.9644001423994304 / (1 - 0.18867924528301888))$

$s_{2} = 53 * (0.9644001423994304 / 0.8113207547169812)$

$s_{2} = 53 \cdot 1.1886792452830188$

$s_{2} = 63$

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： $r = 0.18867924528301888$ 插入几何级数的公式：

$a_{n} = 53 \cdot {0.18867924528301888}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 53$

$a_{2} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{2 - 1} = 53 \cdot {0.18867924528301888}^{1} = 53 \cdot 0.18867924528301888 = 10$

$a_{3} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{3 - 1} = 53 \cdot {0.18867924528301888}^{2} = 53 \cdot 0.0355998576005696 = 1.8867924528301887$

$a_{4} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{4 - 1} = 53 \cdot {0.18867924528301888}^{3} = 53 \cdot 0.006716954264258416 = 0.35599857600569607$

$a_{5} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{5 - 1} = 53 \cdot {0.18867924528301888}^{4} = 53 \cdot 0.0012673498611808333 = 0.06716954264258417$

$a_{6} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{6 - 1} = 53 \cdot {0.18867924528301888}^{5} = 53 \cdot 0.0002391226153171384 = 0.012673498611808335$

$a_{7} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{7 - 1} = 53 \cdot {0.18867924528301888}^{6} = 53 \cdot 4.511747458813932 E - 05 = 0.0023912261531713838$

$a_{8} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{8 - 1} = 53 \cdot {0.18867924528301888}^{7} = 53 \cdot 8.51273105436591 E - 06 = 0.00045117474588139326$

$a_{9} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{9 - 1} = 53 \cdot {0.18867924528301888}^{8} = 53 \cdot 1.6061756706350776 E - 06 = 8.51273105436591 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 53 \cdot {0.18867924528301888}^{10 - 1} = 53 \cdot {0.18867924528301888}^{9} = 53 \cdot 3.0305201332737315 E - 07 = 1.606175670635078 E - 05$

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几何数列