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解答 - 几何数列

公比是：

r = 0.06779661016949153

r=0.06779661016949153

该系列的和是：

s = 126

s=126

此系列的通用形式是：

a_{n} = 118 \cdot {0.06779661016949153}^{n - 1}

a_n=118*0.06779661016949153^(n-1)

这个序列的第n项是：

118, 8, 0.5423728813559322, 0.036771042803792016, 0.002492952054494374, 0.00016901369860978805, 1.1458555837951733 E - 05, 7.768512432509649 E - 07, 5.26678808983705 E - 08, 3.5707037897200335 E - 09

118,8,0.5423728813559322,0.036771042803792016,0.002492952054494374,0.00016901369860978805,1.1458555837951733E-05,7.768512432509649E-07,5.26678808983705E-08,3.5707037897200335E-09

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：

$a_{2} a_{1} = \frac{8}{118} = 0.06779661016949153$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.06779661016949153$

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： $a = 118$ 、公比： $r = 0.06779661016949153$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 118 * ((1 - {0.06779661016949153}^{2}) / (1 - 0.06779661016949153))$

$s_{2} = 118 * ((1 - 0.004596380350474002) / (1 - 0.06779661016949153))$

$s_{2} = 118 * (0.995403619649526 / (1 - 0.06779661016949153))$

$s_{2} = 118 * (0.995403619649526 / 0.9322033898305084)$

$s_{2} = 118 \cdot 1.0677966101694916$

$s_{2} = 126$

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： $a = 118$ 和公比： $r = 0.06779661016949153$ 插入几何级数的公式：

$a_{n} = 118 \cdot {0.06779661016949153}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 118$

$a_{2} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{2 - 1} = 118 \cdot {0.06779661016949153}^{1} = 118 \cdot 0.06779661016949153 = 8$

$a_{3} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{3 - 1} = 118 \cdot {0.06779661016949153}^{2} = 118 \cdot 0.004596380350474002 = 0.5423728813559322$

$a_{4} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{4 - 1} = 118 \cdot {0.06779661016949153}^{3} = 118 \cdot 0.00031161900681179674 = 0.036771042803792016$

$a_{5} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{5 - 1} = 118 \cdot {0.06779661016949153}^{4} = 118 \cdot 2.1126712326223506 E - 05 = 0.002492952054494374$

$a_{6} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{6 - 1} = 118 \cdot {0.06779661016949153}^{5} = 118 \cdot 1.4323194797439665 E - 06 = 0.00016901369860978805$

$a_{7} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{7 - 1} = 118 \cdot {0.06779661016949153}^{6} = 118 \cdot 9.710640540637062 E - 08 = 1.1458555837951733 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{8 - 1} = 118 \cdot {0.06779661016949153}^{7} = 118 \cdot 6.583485112296313 E - 09 = 7.768512432509649 E - 07$

$a_{9} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{9 - 1} = 118 \cdot {0.06779661016949153}^{8} = 118 \cdot 4.4633797371500424 E - 10 = 5.26678808983705 E - 08$

$a_{10} = a_{1} \cdot r^{n - 1} = 118 \cdot {0.06779661016949153}^{10 - 1} = 118 \cdot {0.06779661016949153}^{9} = 118 \cdot 3.0260201607796895 E - 11 = 3.5707037897200335 E - 09$

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几何数列