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解答 - 几何数列

公比是：

r = 0.9157894736842105

r=0.9157894736842105

该系列的和是：

s = 182

s=182

此系列的通用形式是：

a_{n} = 95 \cdot {0.9157894736842105}^{n - 1}

a_n=95*0.9157894736842105^(n-1)

这个序列的第n项是：

95, 87, 79.6736842105263, 72.96432132963989, 66.81995742819652, 61.19301364476944, 56.03991775889412, 51.32076678972409, 46.99901800743153, 43.04120596470045

95,87,79.6736842105263,72.96432132963989,66.81995742819652,61.19301364476944,56.03991775889412,51.32076678972409,46.99901800743153,43.04120596470045

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：

$a_{2} a_{1} = \frac{87}{95} = 0.9157894736842105$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.9157894736842105$

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： $a = 95$ 、公比： $r = 0.9157894736842105$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 95 * ((1 - {0.9157894736842105}^{2}) / (1 - 0.9157894736842105))$

$s_{2} = 95 * ((1 - 0.8386703601108032) / (1 - 0.9157894736842105))$

$s_{2} = 95 * (0.1613296398891968 / (1 - 0.9157894736842105))$

$s_{2} = 95 * (0.1613296398891968 / 0.08421052631578951)$

$s_{2} = 95 \cdot 1.9157894736842112$

$s_{2} = 182.00000000000006$

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： $a = 95$ 和公比： $r = 0.9157894736842105$ 插入几何级数的公式：

$a_{n} = 95 \cdot {0.9157894736842105}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 95$

$a_{2} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{2 - 1} = 95 \cdot {0.9157894736842105}^{1} = 95 \cdot 0.9157894736842105 = 87$

$a_{3} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{3 - 1} = 95 \cdot {0.9157894736842105}^{2} = 95 \cdot 0.8386703601108032 = 79.6736842105263$

$a_{4} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{4 - 1} = 95 \cdot {0.9157894736842105}^{3} = 95 \cdot 0.7680454876804198 = 72.96432132963989$

$a_{5} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{5 - 1} = 95 \cdot {0.9157894736842105}^{4} = 95 \cdot 0.7033679729283844 = 66.81995742819652$

$a_{6} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{6 - 1} = 95 \cdot {0.9157894736842105}^{5} = 95 \cdot 0.6441369857344151 = 61.19301364476944$

$a_{7} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{7 - 1} = 95 \cdot {0.9157894736842105}^{6} = 95 \cdot 0.5898938711462539 = 56.03991775889412$

$a_{8} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{8 - 1} = 95 \cdot {0.9157894736842105}^{7} = 95 \cdot 0.5402185977865693 = 51.32076678972409$

$a_{9} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{9 - 1} = 95 \cdot {0.9157894736842105}^{8} = 95 \cdot 0.4947265053413845 = 46.99901800743153$

$a_{10} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.9157894736842105}^{10 - 1} = 95 \cdot {0.9157894736842105}^{9} = 95 \cdot 0.4530653259442153 = 43.04120596470045$

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