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解答 - 几何数列

公比是：

r = 0.30158730158730157

r=0.30158730158730157

该系列的和是：

s = 82

s=82

此系列的通用形式是：

a_{n} = 63 \cdot {0.30158730158730157}^{n - 1}

a_n=63*0.30158730158730157^(n-1)

这个序列的第n项是：

63, 19, 5.730158730158729, 1.7281431090954897, 0.5211860170287985, 0.15718308450074875, 0.047404422309749616, 0.014296571807702264, 0.004311664513434016, 0.0013003432659562907

63,19,5.730158730158729,1.7281431090954897,0.5211860170287985,0.15718308450074875,0.047404422309749616,0.014296571807702264,0.004311664513434016,0.0013003432659562907

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：

$a_{2} a_{1} = \frac{19}{63} = 0.30158730158730157$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.30158730158730157$

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： $a = 63$ 、公比： $r = 0.30158730158730157$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 63 * ((1 - {0.30158730158730157}^{2}) / (1 - 0.30158730158730157))$

$s_{2} = 63 * ((1 - 0.09095490047871) / (1 - 0.30158730158730157))$

$s_{2} = 63 * (0.90904509952129 / (1 - 0.30158730158730157))$

$s_{2} = 63 * (0.90904509952129 / 0.6984126984126984)$

$s_{2} = 63 \cdot 1.3015873015873016$

$s_{2} = 82$

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： $a = 63$ 和公比： $r = 0.30158730158730157$ 插入几何级数的公式：

$a_{n} = 63 \cdot {0.30158730158730157}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 63$

$a_{2} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{2 - 1} = 63 \cdot {0.30158730158730157}^{1} = 63 \cdot 0.30158730158730157 = 19$

$a_{3} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{3 - 1} = 63 \cdot {0.30158730158730157}^{2} = 63 \cdot 0.09095490047871 = 5.730158730158729$

$a_{4} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{4 - 1} = 63 \cdot {0.30158730158730157}^{3} = 63 \cdot 0.02743084300151571 = 1.7281431090954897$

$a_{5} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{5 - 1} = 63 \cdot {0.30158730158730157}^{4} = 63 \cdot 0.00827279392109204 = 0.5211860170287985$

$a_{6} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{6 - 1} = 63 \cdot {0.30158730158730157}^{5} = 63 \cdot 0.00249496959524998 = 0.15718308450074875$

$a_{7} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{7 - 1} = 63 \cdot {0.30158730158730157}^{6} = 63 \cdot 0.0007524511477738034 = 0.047404422309749616$

$a_{8} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{8 - 1} = 63 \cdot {0.30158730158730157}^{7} = 63 \cdot 0.00022692971123336927 = 0.014296571807702264$

$a_{9} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{9 - 1} = 63 \cdot {0.30158730158730157}^{8} = 63 \cdot 6.84391192608574 E - 05 = 0.004311664513434016$

$a_{10} = a_{1} \cdot r^{n - 1} = 63 \cdot {0.30158730158730157}^{10 - 1} = 63 \cdot {0.30158730158730157}^{9} = 63 \cdot 2.06403693008935 E - 05 = 0.0013003432659562907$

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几何数列