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解答 - 几何数列

公比是：

r = 0.41025641025641024

r=0.41025641025641024

该系列的和是：

s = 54

s=54

此系列的通用形式是：

a_{n} = 39 \cdot {0.41025641025641024}^{n - 1}

a_n=39*0.41025641025641024^(n-1)

这个序列的第n项是：

39, 16, 6.564102564102563, 2.6929651545036157, 1.1048062172322526, 0.4532538327106677, 0.18595029034283803, 0.07628729860218997, 0.03129735327269331, 0.012839939804181874

39,16,6.564102564102563,2.6929651545036157,1.1048062172322526,0.4532538327106677,0.18595029034283803,0.07628729860218997,0.03129735327269331,0.012839939804181874

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：

$a_{2} a_{1} = \frac{16}{39} = 0.41025641025641024$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.41025641025641024$

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： $a = 39$ 、公比： $r = 0.41025641025641024$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 39 * ((1 - {0.41025641025641024}^{2}) / (1 - 0.41025641025641024))$

$s_{2} = 39 * ((1 - 0.16831032215647598) / (1 - 0.41025641025641024))$

$s_{2} = 39 * (0.831689677843524 / (1 - 0.41025641025641024))$

$s_{2} = 39 * (0.831689677843524 / 0.5897435897435898)$

$s_{2} = 39 \cdot 1.4102564102564101$

$s_{2} = 54.99999999999999$

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： $a = 39$ 和公比： $r = 0.41025641025641024$ 插入几何级数的公式：

$a_{n} = 39 \cdot {0.41025641025641024}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 39$

$a_{2} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{2 - 1} = 39 \cdot {0.41025641025641024}^{1} = 39 \cdot 0.41025641025641024 = 16$

$a_{3} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{3 - 1} = 39 \cdot {0.41025641025641024}^{2} = 39 \cdot 0.16831032215647598 = 6.564102564102563$

$a_{4} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{4 - 1} = 39 \cdot {0.41025641025641024}^{3} = 39 \cdot 0.06905038857701579 = 2.6929651545036157$

$a_{5} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{5 - 1} = 39 \cdot {0.41025641025641024}^{4} = 39 \cdot 0.028328364544416732 = 1.1048062172322526$

$a_{6} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{6 - 1} = 39 \cdot {0.41025641025641024}^{5} = 39 \cdot 0.011621893146427377 = 0.4532538327106677$

$a_{7} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{7 - 1} = 39 \cdot {0.41025641025641024}^{6} = 39 \cdot 0.004767956162636872 = 0.18595029034283803$

$a_{8} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{8 - 1} = 39 \cdot {0.41025641025641024}^{7} = 39 \cdot 0.0019560845795433325 = 0.07628729860218997$

$a_{9} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{9 - 1} = 39 \cdot {0.41025641025641024}^{8} = 39 \cdot 0.000802496237761367 = 0.03129735327269331$

$a_{10} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.41025641025641024}^{10 - 1} = 39 \cdot {0.41025641025641024}^{9} = 39 \cdot 0.00032922922574825315 = 0.012839939804181874$

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几何数列