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解答 - 几何数列

公比是：

r = 0.25411522633744854

r=0.25411522633744854

该系列的和是：

s = 1218

s=1218

此系列的通用形式是：

a_{n} = 972 \cdot {0.25411522633744854}^{n - 1}

a_n=972*0.25411522633744854^(n-1)

这个序列的第n项是：

972, 246.99999999999997, 62.76646090534979, 15.949913419363575, 4.053115858624283, 1.0299584537862116, 0.2617281256020517, 0.06650910187624154, 0.016900975476781543, 0.004294795208606009

972,246.99999999999997,62.76646090534979,15.949913419363575,4.053115858624283,1.0299584537862116,0.2617281256020517,0.06650910187624154,0.016900975476781543,0.004294795208606009

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：

$a_{2} a_{1} = \frac{247}{972} = 0.25411522633744854$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.25411522633744854$

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： $a = 972$ 、公比： $r = 0.25411522633744854$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 972 * ((1 - {0.25411522633744854}^{2}) / (1 - 0.25411522633744854))$

$s_{2} = 972 * ((1 - 0.06457454825653271) / (1 - 0.25411522633744854))$

$s_{2} = 972 * (0.9354254517434673 / (1 - 0.25411522633744854))$

$s_{2} = 972 * (0.9354254517434673 / 0.7458847736625515)$

$s_{2} = 972 \cdot 1.2541152263374484$

$s_{2} = 1218.9999999999998$

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： $a = 972$ 和公比： $r = 0.25411522633744854$ 插入几何级数的公式：

$a_{n} = 972 \cdot {0.25411522633744854}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 972$

$a_{2} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{2 - 1} = 972 \cdot {0.25411522633744854}^{1} = 972 \cdot 0.25411522633744854 = 246.99999999999997$

$a_{3} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{3 - 1} = 972 \cdot {0.25411522633744854}^{2} = 972 \cdot 0.06457454825653271 = 62.76646090534979$

$a_{4} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{4 - 1} = 972 \cdot {0.25411522633744854}^{3} = 972 \cdot 0.0164093759458473 = 15.949913419363575$

$a_{5} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{5 - 1} = 972 \cdot {0.25411522633744854}^{4} = 972 \cdot 0.00416987228253527 = 4.053115858624283$

$a_{6} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{6 - 1} = 972 \cdot {0.25411522633744854}^{5} = 972 \cdot 0.0010596280388747033 = 1.0299584537862116$

$a_{7} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{7 - 1} = 972 \cdot {0.25411522633744854}^{6} = 972 \cdot 0.00026926761893215196 = 0.2617281256020517$

$a_{8} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{8 - 1} = 972 \cdot {0.25411522633744854}^{7} = 972 \cdot 6.842500193028965 E - 05 = 0.06650910187624154$

$a_{9} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{9 - 1} = 972 \cdot {0.25411522633744854}^{8} = 972 \cdot 1.7387834852655907 E - 05 = 0.016900975476781543$

$a_{10} = a_{1} \cdot r^{n - 1} = 972 \cdot {0.25411522633744854}^{10 - 1} = 972 \cdot {0.25411522633744854}^{9} = 972 \cdot 4.418513589100832 E - 06 = 0.004294795208606009$

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