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解答 - 几何数列

公比是：

r = - 0.5384615384615384

r=-0.5384615384615384

该系列的和是：

s = 6

s=6

此系列的通用形式是：

a_{n} = 13 \cdot - {0.5384615384615384}^{n - 1}

a_n=13*-0.5384615384615384^(n-1)

这个序列的第n项是：

13, - 7, 3.769230769230769, - 2.0295857988165675, 1.0928538916704595, - 0.588459787822555, 0.31686296267368347, - 0.17061851836275263, 0.09187150988763604, - 0.04946927455488094

13,-7,3.769230769230769,-2.0295857988165675,1.0928538916704595,-0.588459787822555,0.31686296267368347,-0.17061851836275263,0.09187150988763604,-0.04946927455488094

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：

$a_{2} a_{1} = - \frac{7}{13} = - 0.5384615384615384$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 0.5384615384615384$

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： $a = 13$ 、公比： $r = - 0.5384615384615384$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 13 * ((1 - - {0.5384615384615384}^{2}) / (1 - - 0.5384615384615384))$

$s_{2} = 13 * ((1 - 0.28994082840236685) / (1 - - 0.5384615384615384))$

$s_{2} = 13 * (0.7100591715976332 / (1 - - 0.5384615384615384))$

$s_{2} = 13 * (0.7100591715976332 / 1.5384615384615383)$

$s_{2} = 13 \cdot 0.4615384615384616$

$s_{2} = 6.000000000000001$

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： $a = 13$ 和公比： $r = - 0.5384615384615384$ 插入几何级数的公式：

$a_{n} = 13 \cdot - {0.5384615384615384}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 13$

$a_{2} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{2 - 1} = 13 \cdot - {0.5384615384615384}^{1} = 13 \cdot - 0.5384615384615384 = - 7$

$a_{3} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{3 - 1} = 13 \cdot - {0.5384615384615384}^{2} = 13 \cdot 0.28994082840236685 = 3.769230769230769$

$a_{4} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{4 - 1} = 13 \cdot - {0.5384615384615384}^{3} = 13 \cdot - 0.15612198452435136 = - 2.0295857988165675$

$a_{5} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{5 - 1} = 13 \cdot - {0.5384615384615384}^{4} = 13 \cdot 0.08406568397465074 = 1.0928538916704595$

$a_{6} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{6 - 1} = 13 \cdot - {0.5384615384615384}^{5} = 13 \cdot - 0.04526613752481193 = - 0.588459787822555$

$a_{7} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{7 - 1} = 13 \cdot - {0.5384615384615384}^{6} = 13 \cdot 0.024374074051821806 = 0.31686296267368347$

$a_{8} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{8 - 1} = 13 \cdot - {0.5384615384615384}^{7} = 13 \cdot - 0.013124501412519434 = - 0.17061851836275263$

$a_{9} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{9 - 1} = 13 \cdot - {0.5384615384615384}^{8} = 13 \cdot 0.007067039222125849 = 0.09187150988763604$

$a_{10} = a_{1} \cdot r^{n - 1} = 13 \cdot - {0.5384615384615384}^{10 - 1} = 13 \cdot - {0.5384615384615384}^{9} = 13 \cdot - 0.0038053288119139182 = - 0.04946927455488094$

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