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解答 - 几何数列

公比是：

r = 0.9459459459459459

r=0.9459459459459459

该系列的和是：

s = 72

s=72

此系列的通用形式是：

a_{n} = 37 \cdot {0.9459459459459459}^{n - 1}

a_n=37*0.9459459459459459^(n-1)

这个序列的第n项是：

37, 35, 33.108108108108105, 31.318480642804968, 29.62558979724794, 28.024206564964267, 26.509384588479715, 25.076444880994323, 23.72096137391355, 22.4387472455939

37,35,33.108108108108105,31.318480642804968,29.62558979724794,28.024206564964267,26.509384588479715,25.076444880994323,23.72096137391355,22.4387472455939

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：

$a_{2} a_{1} = \frac{35}{37} = 0.9459459459459459$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.9459459459459459$

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： $a = 37$ 、公比： $r = 0.9459459459459459$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 37 * ((1 - {0.9459459459459459}^{2}) / (1 - 0.9459459459459459))$

$s_{2} = 37 * ((1 - 0.8948137326515705) / (1 - 0.9459459459459459))$

$s_{2} = 37 * (0.10518626734842951 / (1 - 0.9459459459459459))$

$s_{2} = 37 * (0.10518626734842951 / 0.05405405405405406)$

$s_{2} = 37 \cdot 1.9459459459459458$

$s_{2} = 72$

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： $a = 37$ 和公比： $r = 0.9459459459459459$ 插入几何级数的公式：

$a_{n} = 37 \cdot {0.9459459459459459}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 37$

$a_{2} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{2 - 1} = 37 \cdot {0.9459459459459459}^{1} = 37 \cdot 0.9459459459459459 = 35$

$a_{3} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{3 - 1} = 37 \cdot {0.9459459459459459}^{2} = 37 \cdot 0.8948137326515705 = 33.108108108108105$

$a_{4} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{4 - 1} = 37 \cdot {0.9459459459459459}^{3} = 37 \cdot 0.8464454227785126 = 31.318480642804968$

$a_{5} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{5 - 1} = 37 \cdot {0.9459459459459459}^{4} = 37 \cdot 0.8006916161418363 = 29.62558979724794$

$a_{6} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{6 - 1} = 37 \cdot {0.9459459459459459}^{5} = 37 \cdot 0.7574109882422775 = 28.024206564964267$

$a_{7} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{7 - 1} = 37 \cdot {0.9459459459459459}^{6} = 37 \cdot 0.716469853742695 = 26.509384588479715$

$a_{8} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{8 - 1} = 37 \cdot {0.9459459459459459}^{7} = 37 \cdot 0.6777417535403871 = 25.076444880994323$

$a_{9} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{9 - 1} = 37 \cdot {0.9459459459459459}^{8} = 37 \cdot 0.6411070641598257 = 23.72096137391355$

$a_{10} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.9459459459459459}^{10 - 1} = 37 \cdot {0.9459459459459459}^{9} = 37 \cdot 0.6064526282592946 = 22.4387472455939$

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