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解答 - 几何数列

公比是：

r = 3.272727272727273

r=3.272727272727273

该系列的和是：

s = 188

s=188

此系列的通用形式是：

a_{n} = 44 \cdot {3.272727272727273}^{n - 1}

a_n=44*3.272727272727273^(n-1)

这个序列的第n项是：

44, 144, 471.27272727272737, 1542.3471074380168, 5047.681442524418, 16519.68472098901, 54064.422723236756, 176938.11073059303, 579070.18057285, 1895138.772783873

44,144,471.27272727272737,1542.3471074380168,5047.681442524418,16519.68472098901,54064.422723236756,176938.11073059303,579070.18057285,1895138.772783873

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：

$a_{2} a_{1} = \frac{144}{44} = 3.272727272727273$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 3.272727272727273$

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： $a = 44$ 、公比： $r = 3.272727272727273$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 44 * ((1 - {3.272727272727273}^{2}) / (1 - 3.272727272727273))$

$s_{2} = 44 * ((1 - 10.710743801652894) / (1 - 3.272727272727273))$

$s_{2} = 44 * (- 9.710743801652894 / (1 - 3.272727272727273))$

$s_{2} = 44 * (- 9.710743801652894 / - 2.272727272727273)$

$s_{2} = 44 \cdot 4.272727272727273$

$s_{2} = 188.00000000000003$

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： $a = 44$ 和公比： $r = 3.272727272727273$ 插入几何级数的公式：

$a_{n} = 44 \cdot {3.272727272727273}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 44$

$a_{2} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{2 - 1} = 44 \cdot {3.272727272727273}^{1} = 44 \cdot 3.272727272727273 = 144$

$a_{3} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{3 - 1} = 44 \cdot {3.272727272727273}^{2} = 44 \cdot 10.710743801652894 = 471.27272727272737$

$a_{4} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{4 - 1} = 44 \cdot {3.272727272727273}^{3} = 44 \cdot 35.05334335086402 = 1542.3471074380168$

$a_{5} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{5 - 1} = 44 \cdot {3.272727272727273}^{4} = 44 \cdot 114.72003278464588 = 5047.681442524418$

$a_{6} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{6 - 1} = 44 \cdot {3.272727272727273}^{5} = 44 \cdot 375.4473800224775 = 16519.68472098901$

$a_{7} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{7 - 1} = 44 \cdot {3.272727272727273}^{6} = 44 \cdot 1228.7368800735626 = 54064.422723236756$

$a_{8} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{8 - 1} = 44 \cdot {3.272727272727273}^{7} = 44 \cdot 4021.320698422569 = 176938.11073059303$

$a_{9} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{9 - 1} = 44 \cdot {3.272727272727273}^{8} = 44 \cdot 13160.685922110228 = 579070.18057285$

$a_{10} = a_{1} \cdot r^{n - 1} = 44 \cdot {3.272727272727273}^{10 - 1} = 44 \cdot {3.272727272727273}^{9} = 44 \cdot 43071.33574508802 = 1895138.772783873$

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