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解答 - 几何数列

公比是：

r = 0.024615384615384615

r=0.024615384615384615

该系列的和是：

s = 1664

s=1664

此系列的通用形式是：

a_{n} = 1625 \cdot {0.024615384615384615}^{n - 1}

a_n=1625*0.024615384615384615^(n-1)

这个序列的第n项是：

1625, 40, 0.9846153846153846, 0.024236686390532544, 0.0005965953573054165, 1.4685424179825638 E - 05, 3.614873644264772 E - 07, 8.89815050895944 E - 09, 2.1903139714361695 E - 10, 5.391542083535187 E - 12

1625,40,0.9846153846153846,0.024236686390532544,0.0005965953573054165,1.4685424179825638E-05,3.614873644264772E-07,8.89815050895944E-09,2.1903139714361695E-10,5.391542083535187E-12

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：

$a_{2} a_{1} = \frac{40}{1625} = 0.024615384615384615$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.024615384615384615$

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： $a = 1, 625$ 、公比： $r = 0.024615384615384615$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1625 * ((1 - {0.024615384615384615}^{2}) / (1 - 0.024615384615384615))$

$s_{2} = 1625 * ((1 - 0.0006059171597633136) / (1 - 0.024615384615384615))$

$s_{2} = 1625 * (0.9993940828402367 / (1 - 0.024615384615384615))$

$s_{2} = 1625 * (0.9993940828402367 / 0.9753846153846154)$

$s_{2} = 1625 \cdot 1.0246153846153845$

$s_{2} = 1664.9999999999998$

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： $a = 1, 625$ 和公比： $r = 0.024615384615384615$ 插入几何级数的公式：

$a_{n} = 1625 \cdot {0.024615384615384615}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1625$

$a_{2} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{2 - 1} = 1625 \cdot {0.024615384615384615}^{1} = 1625 \cdot 0.024615384615384615 = 40$

$a_{3} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{3 - 1} = 1625 \cdot {0.024615384615384615}^{2} = 1625 \cdot 0.0006059171597633136 = 0.9846153846153846$

$a_{4} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{4 - 1} = 1625 \cdot {0.024615384615384615}^{3} = 1625 \cdot 1.4914883932635412 E - 05 = 0.024236686390532544$

$a_{5} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{5 - 1} = 1625 \cdot {0.024615384615384615}^{4} = 1625 \cdot 3.671356044956409 E - 07 = 0.0005965953573054165$

$a_{6} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{6 - 1} = 1625 \cdot {0.024615384615384615}^{5} = 1625 \cdot 9.03718411066193 E - 09 = 1.4685424179825638 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{7 - 1} = 1625 \cdot {0.024615384615384615}^{6} = 1625 \cdot 2.2245376272398596 E - 10 = 3.614873644264772 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{8 - 1} = 1625 \cdot {0.024615384615384615}^{7} = 1625 \cdot 5.475784928590424 E - 12 = 8.89815050895944 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{9 - 1} = 1625 \cdot {0.024615384615384615}^{8} = 1625 \cdot 1.3478855208837967 E - 13 = 2.1903139714361695 E - 10$

$a_{10} = a_{1} \cdot r^{n - 1} = 1625 \cdot {0.024615384615384615}^{10 - 1} = 1625 \cdot {0.024615384615384615}^{9} = 1625 \cdot 3.317872051406269 E - 15 = 5.391542083535187 E - 12$

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几何数列