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解答 - 几何数列

公比是：

r = 0.0449438202247191

r=0.0449438202247191

该系列的和是：

s = 837

s=837

此系列的通用形式是：

a_{n} = 801 \cdot {0.0449438202247191}^{n - 1}

a_n=801*0.0449438202247191^(n-1)

这个序列的第n项是：

801, 36, 1.6179775280898876, 0.07271809115010731, 0.0032682288157351597, 0.00014688668834764762, 6.601648914501017 E - 06, 2.9670332200004567 E - 07, 1.3334980764046995 E - 08, 5.993249781594155 E - 10

801,36,1.6179775280898876,0.07271809115010731,0.0032682288157351597,0.00014688668834764762,6.601648914501017E-06,2.9670332200004567E-07,1.3334980764046995E-08,5.993249781594155E-10

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：

$a_{2} a_{1} = \frac{36}{801} = 0.0449438202247191$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0449438202247191$

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： $a = 801$ 、公比： $r = 0.0449438202247191$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 801 * ((1 - {0.0449438202247191}^{2}) / (1 - 0.0449438202247191))$

$s_{2} = 801 * ((1 - 0.0020199469763918696) / (1 - 0.0449438202247191))$

$s_{2} = 801 * (0.9979800530236081 / (1 - 0.0449438202247191))$

$s_{2} = 801 * (0.9979800530236081 / 0.9550561797752809)$

$s_{2} = 801 \cdot 1.0449438202247192$

$s_{2} = 837.0000000000001$

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： $a = 801$ 和公比： $r = 0.0449438202247191$ 插入几何级数的公式：

$a_{n} = 801 \cdot {0.0449438202247191}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 801$

$a_{2} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{2 - 1} = 801 \cdot {0.0449438202247191}^{1} = 801 \cdot 0.0449438202247191 = 36$

$a_{3} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{3 - 1} = 801 \cdot {0.0449438202247191}^{2} = 801 \cdot 0.0020199469763918696 = 1.6179775280898876$

$a_{4} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{4 - 1} = 801 \cdot {0.0449438202247191}^{3} = 801 \cdot 9.078413377042111 E - 05 = 0.07271809115010731$

$a_{5} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{5 - 1} = 801 \cdot {0.0449438202247191}^{4} = 801 \cdot 4.080185787434656 E - 06 = 0.0032682288157351597$

$a_{6} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{6 - 1} = 801 \cdot {0.0449438202247191}^{5} = 801 \cdot 1.8337913651391713 E - 07 = 0.00014688668834764762$

$a_{7} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{7 - 1} = 801 \cdot {0.0449438202247191}^{6} = 801 \cdot 8.241758944445714 E - 09 = 6.601648914501017 E - 06$

$a_{8} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{8 - 1} = 801 \cdot {0.0449438202247191}^{7} = 801 \cdot 3.704161323346388 E - 10 = 2.9670332200004567 E - 07$

$a_{9} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{9 - 1} = 801 \cdot {0.0449438202247191}^{8} = 801 \cdot 1.6647916059983766 E - 11 = 1.3334980764046995 E - 08$

$a_{10} = a_{1} \cdot r^{n - 1} = 801 \cdot {0.0449438202247191}^{10 - 1} = 801 \cdot {0.0449438202247191}^{9} = 801 \cdot 7.482209465161242 E - 13 = 5.993249781594155 E - 10$

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几何数列