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解答 - 几何数列

公比是：

r = 0.2545454545454545

r=0.2545454545454545

该系列的和是：

s = 69

s=69

此系列的通用形式是：

a_{n} = 55 \cdot {0.2545454545454545}^{n - 1}

a_n=55*0.2545454545454545^(n-1)

这个序列的第n项是：

55, 13.999999999999998, 3.5636363636363626, 0.9071074380165286, 0.23090007513148, 0.05877456457892217, 0.014960798256452917, 0.003808203192551651, 0.000969360812649511, 0.00024674638867442093

55,13.999999999999998,3.5636363636363626,0.9071074380165286,0.23090007513148,0.05877456457892217,0.014960798256452917,0.003808203192551651,0.000969360812649511,0.00024674638867442093

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：

$a_{2} a_{1} = \frac{14}{55} = 0.2545454545454545$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.2545454545454545$

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： $a = 55$ 、公比： $r = 0.2545454545454545$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 55 * ((1 - {0.2545454545454545}^{2}) / (1 - 0.2545454545454545))$

$s_{2} = 55 * ((1 - 0.06479338842975205) / (1 - 0.2545454545454545))$

$s_{2} = 55 * (0.935206611570248 / (1 - 0.2545454545454545))$

$s_{2} = 55 * (0.935206611570248 / 0.7454545454545455)$

$s_{2} = 55 \cdot 1.2545454545454546$

$s_{2} = 69$

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： $a = 55$ 和公比： $r = 0.2545454545454545$ 插入几何级数的公式：

$a_{n} = 55 \cdot {0.2545454545454545}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 55$

$a_{2} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{2 - 1} = 55 \cdot {0.2545454545454545}^{1} = 55 \cdot 0.2545454545454545 = 13.999999999999998$

$a_{3} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{3 - 1} = 55 \cdot {0.2545454545454545}^{2} = 55 \cdot 0.06479338842975205 = 3.5636363636363626$

$a_{4} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{4 - 1} = 55 \cdot {0.2545454545454545}^{3} = 55 \cdot 0.01649286250939143 = 0.9071074380165286$

$a_{5} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{5 - 1} = 55 \cdot {0.2545454545454545}^{4} = 55 \cdot 0.0041981831842087276 = 0.23090007513148$

$a_{6} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{6 - 1} = 55 \cdot {0.2545454545454545}^{5} = 55 \cdot 0.001068628446889494 = 0.05877456457892217$

$a_{7} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{7 - 1} = 55 \cdot {0.2545454545454545}^{6} = 55 \cdot 0.0002720145137536894 = 0.014960798256452917$

$a_{8} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{8 - 1} = 55 \cdot {0.2545454545454545}^{7} = 55 \cdot 6.924005804639365 E - 05 = 0.003808203192551651$

$a_{9} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{9 - 1} = 55 \cdot {0.2545454545454545}^{8} = 55 \cdot 1.7624742048172928 E - 05 = 0.000969360812649511$

$a_{10} = a_{1} \cdot r^{n - 1} = 55 \cdot {0.2545454545454545}^{10 - 1} = 55 \cdot {0.2545454545454545}^{9} = 55 \cdot 4.486297975898563 E - 06 = 0.00024674638867442093$

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