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解答 - 几何数列

公比是：

r = 0.13385826771653545

r=0.13385826771653545

该系列的和是：

s = 288

s=288

此系列的通用形式是：

a_{n} = 254 \cdot {0.13385826771653545}^{n - 1}

a_n=254*0.13385826771653545^(n-1)

这个序列的第n项是：

254, 34, 4.5511811023622055, 0.6092132184264369, 0.08154822608857819, 0.010915904279573459, 0.001461184037423219, 0.0001955915640645254, 2.6181547945645138 E - 05, 3.504616654141475 E - 06

254,34,4.5511811023622055,0.6092132184264369,0.08154822608857819,0.010915904279573459,0.001461184037423219,0.0001955915640645254,2.6181547945645138E-05,3.504616654141475E-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：

$a_{2} a_{1} = \frac{34}{254} = 0.13385826771653545$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.13385826771653545$

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： $a = 254$ 、公比： $r = 0.13385826771653545$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 254 * ((1 - {0.13385826771653545}^{2}) / (1 - 0.13385826771653545))$

$s_{2} = 254 * ((1 - 0.017918035836071676) / (1 - 0.13385826771653545))$

$s_{2} = 254 * (0.9820819641639283 / (1 - 0.13385826771653545))$

$s_{2} = 254 * (0.9820819641639283 / 0.8661417322834646)$

$s_{2} = 254 \cdot 1.1338582677165354$

$s_{2} = 288$

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： $a = 254$ 和公比： $r = 0.13385826771653545$ 插入几何级数的公式：

$a_{n} = 254 \cdot {0.13385826771653545}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 254$

$a_{2} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{2 - 1} = 254 \cdot {0.13385826771653545}^{1} = 254 \cdot 0.13385826771653545 = 34$

$a_{3} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{3 - 1} = 254 \cdot {0.13385826771653545}^{2} = 254 \cdot 0.017918035836071676 = 4.5511811023622055$

$a_{4} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{4 - 1} = 254 \cdot {0.13385826771653545}^{3} = 254 \cdot 0.002398477237899358 = 0.6092132184264369$

$a_{5} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{5 - 1} = 254 \cdot {0.13385826771653545}^{4} = 254 \cdot 0.0003210560082227488 = 0.08154822608857819$

$a_{6} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{6 - 1} = 254 \cdot {0.13385826771653545}^{5} = 254 \cdot 4.297600110068291 E - 05 = 0.010915904279573459$

$a_{7} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{7 - 1} = 254 \cdot {0.13385826771653545}^{6} = 254 \cdot 5.752693060721335 E - 06 = 0.001461184037423219$

$a_{8} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{8 - 1} = 254 \cdot {0.13385826771653545}^{7} = 254 \cdot 7.700455278130921 E - 07 = 0.0001955915640645254$

$a_{9} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{9 - 1} = 254 \cdot {0.13385826771653545}^{8} = 254 \cdot 1.0307696041592574 E - 07 = 2.6181547945645138 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 254 \cdot {0.13385826771653545}^{10 - 1} = 254 \cdot {0.13385826771653545}^{9} = 254 \cdot 1.3797703362761714 E - 08 = 3.504616654141475 E - 06$

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