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解答 - 几何数列

公比是：

r = - 0.6363636363636364

r=-0.6363636363636364

该系列的和是：

s = - 16

s=-16

此系列的通用形式是：

a_{n} = - 44 \cdot - {0.6363636363636364}^{n - 1}

a_n=-44*-0.6363636363636364^(n-1)

这个序列的第n项是：

- 44, 28, - 17.818181818181817, 11.33884297520661, - 7.215627347858753, 4.5917628577282965, - 2.922030909463462, 1.859474215113112, - 1.1833017732537985, 0.7530102193433263

-44,28,-17.818181818181817,11.33884297520661,-7.215627347858753,4.5917628577282965,-2.922030909463462,1.859474215113112,-1.1833017732537985,0.7530102193433263

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：

$a_{2} a_{1} = \frac{28}{-} 44 = - 0.6363636363636364$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 0.6363636363636364$

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： $a = - 44$ 、公比： $r = - 0.6363636363636364$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = - 44 * ((1 - - {0.6363636363636364}^{2}) / (1 - - 0.6363636363636364))$

$s_{2} = - 44 * ((1 - 0.4049586776859504) / (1 - - 0.6363636363636364))$

$s_{2} = - 44 * (0.5950413223140496 / (1 - - 0.6363636363636364))$

$s_{2} = - 44 * (0.5950413223140496 / 1.6363636363636362)$

$s_{2} = - 44 \cdot 0.36363636363636365$

$s_{2} = - 16$

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： $a = - 44$ 和公比： $r = - 0.6363636363636364$ 插入几何级数的公式：

$a_{n} = - 44 \cdot - {0.6363636363636364}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = - 44$

$a_{2} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{2 - 1} = - 44 \cdot - {0.6363636363636364}^{1} = - 44 \cdot - 0.6363636363636364 = 28$

$a_{3} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{3 - 1} = - 44 \cdot - {0.6363636363636364}^{2} = - 44 \cdot 0.4049586776859504 = - 17.818181818181817$

$a_{4} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{4 - 1} = - 44 \cdot - {0.6363636363636364}^{3} = - 44 \cdot - 0.25770097670924114 = 11.33884297520661$

$a_{5} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{5 - 1} = - 44 \cdot - {0.6363636363636364}^{4} = - 44 \cdot 0.16399153063315347 = - 7.215627347858753$

$a_{6} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{6 - 1} = - 44 \cdot - {0.6363636363636364}^{5} = - 44 \cdot - 0.1043582467665522 = 4.5917628577282965$

$a_{7} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{7 - 1} = - 44 \cdot - {0.6363636363636364}^{6} = - 44 \cdot 0.06640979339689686 = - 2.922030909463462$

$a_{8} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{8 - 1} = - 44 \cdot - {0.6363636363636364}^{7} = - 44 \cdot - 0.04226077761620709 = 1.859474215113112$

$a_{9} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{9 - 1} = - 44 \cdot - {0.6363636363636364}^{8} = - 44 \cdot 0.026893222119404512 = - 1.1833017732537985$

$a_{10} = a_{1} \cdot r^{n - 1} = - 44 \cdot - {0.6363636363636364}^{10 - 1} = - 44 \cdot - {0.6363636363636364}^{9} = - 44 \cdot - 0.017113868621439234 = 0.7530102193433263$

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