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解答 - 几何数列

公比是：

r = 0.18461538461538463

r=0.18461538461538463

该系列的和是：

s = 308

s=308

此系列的通用形式是：

a_{n} = 260 \cdot {0.18461538461538463}^{n - 1}

a_n=260*0.18461538461538463^(n-1)

这个序列的第n项是：

260, 48, 8.861538461538462, 1.635976331360947, 0.30202639963586714, 0.05575871993277548, 0.010293917526050859, 0.0019004155432709277, 0.00035084594645001744, 6.477155934461862 E - 05

260,48,8.861538461538462,1.635976331360947,0.30202639963586714,0.05575871993277548,0.010293917526050859,0.0019004155432709277,0.00035084594645001744,6.477155934461862E-05

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：

$a_{2} a_{1} = \frac{48}{260} = 0.18461538461538463$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.18461538461538463$

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： $a = 260$ 、公比： $r = 0.18461538461538463$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 260 * ((1 - {0.18461538461538463}^{2}) / (1 - 0.18461538461538463))$

$s_{2} = 260 * ((1 - 0.034082840236686396) / (1 - 0.18461538461538463))$

$s_{2} = 260 * (0.9659171597633136 / (1 - 0.18461538461538463))$

$s_{2} = 260 * (0.9659171597633136 / 0.8153846153846154)$

$s_{2} = 260 \cdot 1.1846153846153846$

$s_{2} = 308$

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： $a = 260$ 和公比： $r = 0.18461538461538463$ 插入几何级数的公式：

$a_{n} = 260 \cdot {0.18461538461538463}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 260$

$a_{2} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{2 - 1} = 260 \cdot {0.18461538461538463}^{1} = 260 \cdot 0.18461538461538463 = 48$

$a_{3} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{3 - 1} = 260 \cdot {0.18461538461538463}^{2} = 260 \cdot 0.034082840236686396 = 8.861538461538462$

$a_{4} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{4 - 1} = 260 \cdot {0.18461538461538463}^{3} = 260 \cdot 0.006292216659080565 = 1.635976331360947$

$a_{5} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{5 - 1} = 260 \cdot {0.18461538461538463}^{4} = 260 \cdot 0.001161639998599489 = 0.30202639963586714$

$a_{6} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{6 - 1} = 260 \cdot {0.18461538461538463}^{5} = 260 \cdot 0.00021445661512605954 = 0.05575871993277548$

$a_{7} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{7 - 1} = 260 \cdot {0.18461538461538463}^{6} = 260 \cdot 3.959199048481099 E - 05 = 0.010293917526050859$

$a_{8} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{8 - 1} = 260 \cdot {0.18461538461538463}^{7} = 260 \cdot 7.3092905510420295 E - 06 = 0.0019004155432709277$

$a_{9} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{9 - 1} = 260 \cdot {0.18461538461538463}^{8} = 260 \cdot 1.349407486346221 E - 06 = 0.00035084594645001744$

$a_{10} = a_{1} \cdot r^{n - 1} = 260 \cdot {0.18461538461538463}^{10 - 1} = 260 \cdot {0.18461538461538463}^{9} = 260 \cdot 2.49121382094687 E - 07 = 6.477155934461862 E - 05$

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几何数列