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解答 - 几何数列

公比是：

r = 0.16049382716049382

r=0.16049382716049382

该系列的和是：

s = 94

s=94

此系列的通用形式是：

a_{n} = 81 \cdot {0.16049382716049382}^{n - 1}

a_n=81*0.16049382716049382^(n-1)

这个序列的第n项是：

81, 13, 2.0864197530864197, 0.334857491236092, 0.05374256032184193, 0.00862534918745611, 0.0013843153016904867, 0.00022217406076513986, 3.565756530798541 E - 05, 5.72281912350383 E - 06

81,13,2.0864197530864197,0.334857491236092,0.05374256032184193,0.00862534918745611,0.0013843153016904867,0.00022217406076513986,3.565756530798541E-05,5.72281912350383E-06

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：

$a_{2} a_{1} = \frac{13}{81} = 0.16049382716049382$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.16049382716049382$

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： $a = 81$ 、公比： $r = 0.16049382716049382$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 81 * ((1 - {0.16049382716049382}^{2}) / (1 - 0.16049382716049382))$

$s_{2} = 81 * ((1 - 0.025758268556622464) / (1 - 0.16049382716049382))$

$s_{2} = 81 * (0.9742417314433776 / (1 - 0.16049382716049382))$

$s_{2} = 81 * (0.9742417314433776 / 0.8395061728395061)$

$s_{2} = 81 \cdot 1.1604938271604939$

$s_{2} = 94$

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： $a = 81$ 和公比： $r = 0.16049382716049382$ 插入几何级数的公式：

$a_{n} = 81 \cdot {0.16049382716049382}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 81$

$a_{2} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{2 - 1} = 81 \cdot {0.16049382716049382}^{1} = 81 \cdot 0.16049382716049382 = 13$

$a_{3} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{3 - 1} = 81 \cdot {0.16049382716049382}^{2} = 81 \cdot 0.025758268556622464 = 2.0864197530864197$

$a_{4} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{4 - 1} = 81 \cdot {0.16049382716049382}^{3} = 81 \cdot 0.004134043101680148 = 0.334857491236092$

$a_{5} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{5 - 1} = 81 \cdot {0.16049382716049382}^{4} = 81 \cdot 0.0006634883990350855 = 0.05374256032184193$

$a_{6} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{6 - 1} = 81 \cdot {0.16049382716049382}^{5} = 81 \cdot 0.00010648579243772976 = 0.00862534918745611$

$a_{7} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{7 - 1} = 81 \cdot {0.16049382716049382}^{6} = 81 \cdot 1.709031236654922 E - 05 = 0.0013843153016904867$

$a_{8} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{8 - 1} = 81 \cdot {0.16049382716049382}^{7} = 81 \cdot 2.742889639075801 E - 06 = 0.00022217406076513986$

$a_{9} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{9 - 1} = 81 \cdot {0.16049382716049382}^{8} = 81 \cdot 4.402168556541408 E - 07 = 3.565756530798541 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 81 \cdot {0.16049382716049382}^{10 - 1} = 81 \cdot {0.16049382716049382}^{9} = 81 \cdot 7.065208794449173 E - 08 = 5.72281912350383 E - 06$

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