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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 = 93

s=93

此系列的通用形式是：

a_{n} = 89 \cdot {0.0449438202247191}^{n - 1}

a_n=89*0.0449438202247191^(n-1)

这个序列的第n项是：

89, 4, 0.1797752808988764, 0.008079787905567478, 0.00036313653508168443, 1.6320743149738625 E - 05, 7.335165460556685 E - 07, 3.296703577778285 E - 08, 1.481664529338555 E - 09, 6.659166423993506 E - 11

89,4,0.1797752808988764,0.008079787905567478,0.00036313653508168443,1.6320743149738625E-05,7.335165460556685E-07,3.296703577778285E-08,1.481664529338555E-09,6.659166423993506E-11

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：

$a_{2} a_{1} = \frac{4}{89} = 0.0449438202247191$

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： $a = 89$ 、公比： $r = 0.0449438202247191$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 89 * ((1 - {0.0449438202247191}^{2}) / (1 - 0.0449438202247191))$

$s_{2} = 89 * ((1 - 0.0020199469763918696) / (1 - 0.0449438202247191))$

$s_{2} = 89 * (0.9979800530236081 / (1 - 0.0449438202247191))$

$s_{2} = 89 * (0.9979800530236081 / 0.9550561797752809)$

$s_{2} = 89 \cdot 1.0449438202247192$

$s_{2} = 93.00000000000001$

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： $a = 89$ 和公比： $r = 0.0449438202247191$ 插入几何级数的公式：

$a_{n} = 89 \cdot {0.0449438202247191}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 89$

$a_{2} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{2 - 1} = 89 \cdot {0.0449438202247191}^{1} = 89 \cdot 0.0449438202247191 = 4$

$a_{3} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{3 - 1} = 89 \cdot {0.0449438202247191}^{2} = 89 \cdot 0.0020199469763918696 = 0.1797752808988764$

$a_{4} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{4 - 1} = 89 \cdot {0.0449438202247191}^{3} = 89 \cdot 9.078413377042111 E - 05 = 0.008079787905567478$

$a_{5} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{5 - 1} = 89 \cdot {0.0449438202247191}^{4} = 89 \cdot 4.080185787434656 E - 06 = 0.00036313653508168443$

$a_{6} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{6 - 1} = 89 \cdot {0.0449438202247191}^{5} = 89 \cdot 1.8337913651391713 E - 07 = 1.6320743149738625 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{7 - 1} = 89 \cdot {0.0449438202247191}^{6} = 89 \cdot 8.241758944445714 E - 09 = 7.335165460556685 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{8 - 1} = 89 \cdot {0.0449438202247191}^{7} = 89 \cdot 3.704161323346388 E - 10 = 3.296703577778285 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{9 - 1} = 89 \cdot {0.0449438202247191}^{8} = 89 \cdot 1.6647916059983766 E - 11 = 1.481664529338555 E - 09$

$a_{10} = a_{1} \cdot r^{n - 1} = 89 \cdot {0.0449438202247191}^{10 - 1} = 89 \cdot {0.0449438202247191}^{9} = 89 \cdot 7.482209465161242 E - 13 = 6.659166423993506 E - 11$

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几何数列