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解答 - 几何数列

公比是：

r = 0.8441558441558441

r=0.8441558441558441

该系列的和是：

s = 142

s=142

此系列的通用形式是：

a_{n} = 77 \cdot {0.8441558441558441}^{n - 1}

a_n=77*0.8441558441558441^(n-1)

这个序列的第n项是：

77, 65, 54.87012987012986, 46.31894079946027, 39.100404570972955, 33.0068350274447, 27.862912685505265, 23.520640578673273, 19.855086202776135, 16.760787054291544

77,65,54.87012987012986,46.31894079946027,39.100404570972955,33.0068350274447,27.862912685505265,23.520640578673273,19.855086202776135,16.760787054291544

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：

$a_{2} a_{1} = \frac{65}{77} = 0.8441558441558441$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.8441558441558441$

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： $a = 77$ 、公比： $r = 0.8441558441558441$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 77 * ((1 - {0.8441558441558441}^{2}) / (1 - 0.8441558441558441))$

$s_{2} = 77 * ((1 - 0.7125990892224657) / (1 - 0.8441558441558441))$

$s_{2} = 77 * (0.28740091077753427 / (1 - 0.8441558441558441))$

$s_{2} = 77 * (0.28740091077753427 / 0.1558441558441559)$

$s_{2} = 77 \cdot 1.8441558441558443$

$s_{2} = 142$

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： $a = 77$ 和公比： $r = 0.8441558441558441$ 插入几何级数的公式：

$a_{n} = 77 \cdot {0.8441558441558441}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 77$

$a_{2} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{2 - 1} = 77 \cdot {0.8441558441558441}^{1} = 77 \cdot 0.8441558441558441 = 65$

$a_{3} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{3 - 1} = 77 \cdot {0.8441558441558441}^{2} = 77 \cdot 0.7125990892224657 = 54.87012987012986$

$a_{4} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{4 - 1} = 77 \cdot {0.8441558441558441}^{3} = 77 \cdot 0.6015446857072763 = 46.31894079946027$

$a_{5} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{5 - 1} = 77 \cdot {0.8441558441558441}^{4} = 77 \cdot 0.5077974619606878 = 39.100404570972955$

$a_{6} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{6 - 1} = 77 \cdot {0.8441558441558441}^{5} = 77 \cdot 0.42866019516161946 = 33.0068350274447$

$a_{7} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{7 - 1} = 77 \cdot {0.8441558441558441}^{6} = 77 \cdot 0.3618560089026658 = 27.862912685505265$

$a_{8} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{8 - 1} = 77 \cdot {0.8441558441558441}^{7} = 77 \cdot 0.30546286465809447 = 23.520640578673273$

$a_{9} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{9 - 1} = 77 \cdot {0.8441558441558441}^{8} = 77 \cdot 0.25785826237371606 = 19.855086202776135$

$a_{10} = a_{1} \cdot r^{n - 1} = 77 \cdot {0.8441558441558441}^{10 - 1} = 77 \cdot {0.8441558441558441}^{9} = 77 \cdot 0.21767255914664344 = 16.760787054291544$

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