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解答 - 几何数列

公比是：

r = 0.13636363636363635

r=0.13636363636363635

该系列的和是：

s = 4250

s=4250

此系列的通用形式是：

a_{n} = 3740 \cdot {0.13636363636363635}^{n - 1}

a_n=3740*0.13636363636363635^(n-1)

这个序列的第n项是：

3740, 509.99999999999994, 69.54545454545453, 9.483471074380162, 1.2932006010518404, 0.1763455365070691, 0.02404711861460033, 0.0032791525383545905, 0.0004471571643210805, 6.0975976952874615 E - 05

3740,509.99999999999994,69.54545454545453,9.483471074380162,1.2932006010518404,0.1763455365070691,0.02404711861460033,0.0032791525383545905,0.0004471571643210805,6.0975976952874615E-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：

$a_{2} a_{1} = \frac{510}{3740} = 0.13636363636363635$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.13636363636363635$

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： $a = 3, 740$ 、公比： $r = 0.13636363636363635$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 3740 * ((1 - {0.13636363636363635}^{2}) / (1 - 0.13636363636363635))$

$s_{2} = 3740 * ((1 - 0.018595041322314047) / (1 - 0.13636363636363635))$

$s_{2} = 3740 * (0.981404958677686 / (1 - 0.13636363636363635))$

$s_{2} = 3740 * (0.981404958677686 / 0.8636363636363636)$

$s_{2} = 3740 \cdot 1.1363636363636365$

$s_{2} = 4250$

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： $a = 3, 740$ 和公比： $r = 0.13636363636363635$ 插入几何级数的公式：

$a_{n} = 3740 \cdot {0.13636363636363635}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 3740$

$a_{2} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{2 - 1} = 3740 \cdot {0.13636363636363635}^{1} = 3740 \cdot 0.13636363636363635 = 509.99999999999994$

$a_{3} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{3 - 1} = 3740 \cdot {0.13636363636363635}^{2} = 3740 \cdot 0.018595041322314047 = 69.54545454545453$

$a_{4} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{4 - 1} = 3740 \cdot {0.13636363636363635}^{3} = 3740 \cdot 0.002535687453042824 = 9.483471074380162$

$a_{5} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{5 - 1} = 3740 \cdot {0.13636363636363635}^{4} = 3740 \cdot 0.00034577556177856696 = 1.2932006010518404$

$a_{6} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{6 - 1} = 3740 \cdot {0.13636363636363635}^{5} = 3740 \cdot 4.7151212969804575 E - 05 = 0.1763455365070691$

$a_{7} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{7 - 1} = 3740 \cdot {0.13636363636363635}^{6} = 3740 \cdot 6.429710859518805 E - 06 = 0.02404711861460033$

$a_{8} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{8 - 1} = 3740 \cdot {0.13636363636363635}^{7} = 3740 \cdot 8.767787535707462 E - 07 = 0.0032791525383545905$

$a_{9} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{9 - 1} = 3740 \cdot {0.13636363636363635}^{8} = 3740 \cdot 1.1956073912328355 E - 07 = 0.0004471571643210805$

$a_{10} = a_{1} \cdot r^{n - 1} = 3740 \cdot {0.13636363636363635}^{10 - 1} = 3740 \cdot {0.13636363636363635}^{9} = 3740 \cdot 1.630373715317503 E - 08 = 6.0975976952874615 E - 05$

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几何数列