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解答 - 几何数列

公比是：

r = - 1.1363636363636365

r=-1.1363636363636365

该系列的和是：

s = 3

s=3

此系列的通用形式是：

a_{n} = - 22 \cdot - {1.1363636363636365}^{n - 1}

a_n=-22*-1.1363636363636365^(n-1)

这个序列的第n项是：

- 22, 25.000000000000004, - 28.409090909090917, 32.28305785123968, - 36.68529301277237, 41.687832969059514, - 47.372537464840356, 53.832428937318596, - 61.17321470149841, 69.51501670624819

-22,25.000000000000004,-28.409090909090917,32.28305785123968,-36.68529301277237,41.687832969059514,-47.372537464840356,53.832428937318596,-61.17321470149841,69.51501670624819

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：

$a_{2} a_{1} = \frac{25}{-} 22 = - 1.1363636363636365$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 1.1363636363636365$

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： $a = - 22$ 、公比： $r = - 1.1363636363636365$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = - 22 * ((1 - - {1.1363636363636365}^{2}) / (1 - - 1.1363636363636365))$

$s_{2} = - 22 * ((1 - 1.291322314049587) / (1 - - 1.1363636363636365))$

$s_{2} = - 22 * (- 0.2913223140495871 / (1 - - 1.1363636363636365))$

$s_{2} = - 22 * (- 0.2913223140495871 / 2.1363636363636367)$

$s_{2} = - 22 \cdot - 0.1363636363636365$

$s_{2} = 3.0000000000000027$

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： $a = - 22$ 和公比： $r = - 1.1363636363636365$ 插入几何级数的公式：

$a_{n} = - 22 \cdot - {1.1363636363636365}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = - 22$

$a_{2} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{2 - 1} = - 22 \cdot - {1.1363636363636365}^{1} = - 22 \cdot - 1.1363636363636365 = 25.000000000000004$

$a_{3} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{3 - 1} = - 22 \cdot - {1.1363636363636365}^{2} = - 22 \cdot 1.291322314049587 = - 28.409090909090917$

$a_{4} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{4 - 1} = - 22 \cdot - {1.1363636363636365}^{3} = - 22 \cdot - 1.4674117205108945 = 32.28305785123968$

$a_{5} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{5 - 1} = - 22 \cdot - {1.1363636363636365}^{4} = - 22 \cdot 1.6675133187623803 = - 36.68529301277237$

$a_{6} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{6 - 1} = - 22 \cdot - {1.1363636363636365}^{5} = - 22 \cdot - 1.8949014985936141 = 41.687832969059514$

$a_{7} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{7 - 1} = - 22 \cdot - {1.1363636363636365}^{6} = - 22 \cdot 2.1532971574927435 = - 47.372537464840356$

$a_{8} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{8 - 1} = - 22 \cdot - {1.1363636363636365}^{7} = - 22 \cdot - 2.446928588059936 = 53.832428937318596$

$a_{9} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{9 - 1} = - 22 \cdot - {1.1363636363636365}^{8} = - 22 \cdot 2.7806006682499276 = - 61.17321470149841$

$a_{10} = a_{1} \cdot r^{n - 1} = - 22 \cdot - {1.1363636363636365}^{10 - 1} = - 22 \cdot - {1.1363636363636365}^{9} = - 22 \cdot - 3.1597734866476452 = 69.51501670624819$

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