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解答 - 几何数列

公比是：

r = - 1.7272727272727273

r=-1.7272727272727273

该系列的和是：

s = - 7

s=-7

此系列的通用形式是：

a_{n} = 11 \cdot - {1.7272727272727273}^{n - 1}

a_n=11*-1.7272727272727273^(n-1)

这个序列的第n项是：

11, - 19, 32.81818181818182, - 56.685950413223146, 97.91209616829451, - 169.12089338159961, 292.11790675003573, - 504.56729347733443, 871.525325097214, - 1505.3619251679152

11,-19,32.81818181818182,-56.685950413223146,97.91209616829451,-169.12089338159961,292.11790675003573,-504.56729347733443,871.525325097214,-1505.3619251679152

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：

$a_{2} a_{1} = - \frac{19}{11} = - 1.7272727272727273$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 1.7272727272727273$

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： $a = 11$ 、公比： $r = - 1.7272727272727273$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 11 * ((1 - - {1.7272727272727273}^{2}) / (1 - - 1.7272727272727273))$

$s_{2} = 11 * ((1 - 2.9834710743801653) / (1 - - 1.7272727272727273))$

$s_{2} = 11 * (- 1.9834710743801653 / (1 - - 1.7272727272727273))$

$s_{2} = 11 * (- 1.9834710743801653 / 2.7272727272727275)$

$s_{2} = 11 \cdot - 0.7272727272727272$

$s_{2} = - 7.999999999999999$

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： $a = 11$ 和公比： $r = - 1.7272727272727273$ 插入几何级数的公式：

$a_{n} = 11 \cdot - {1.7272727272727273}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 11$

$a_{2} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{2 - 1} = 11 \cdot - {1.7272727272727273}^{1} = 11 \cdot - 1.7272727272727273 = - 19$

$a_{3} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{3 - 1} = 11 \cdot - {1.7272727272727273}^{2} = 11 \cdot 2.9834710743801653 = 32.81818181818182$

$a_{4} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{4 - 1} = 11 \cdot - {1.7272727272727273}^{3} = 11 \cdot - 5.153268219383922 = - 56.685950413223146$

$a_{5} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{5 - 1} = 11 \cdot - {1.7272727272727273}^{4} = 11 \cdot 8.901099651663138 = 97.91209616829451$

$a_{6} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{6 - 1} = 11 \cdot - {1.7272727272727273}^{5} = 11 \cdot - 15.37462667105451 = - 169.12089338159961$

$a_{7} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{7 - 1} = 11 \cdot - {1.7272727272727273}^{6} = 11 \cdot 26.556173340912338 = 292.11790675003573$

$a_{8} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{8 - 1} = 11 \cdot - {1.7272727272727273}^{7} = 11 \cdot - 45.86975395248495 = - 504.56729347733443$

$a_{9} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{9 - 1} = 11 \cdot - {1.7272727272727273}^{8} = 11 \cdot 79.22957500883764 = 871.525325097214$

$a_{10} = a_{1} \cdot r^{n - 1} = 11 \cdot - {1.7272727272727273}^{10 - 1} = 11 \cdot - {1.7272727272727273}^{9} = 11 \cdot - 136.8510841061741 = - 1505.3619251679152$

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几何数列