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解答 - 几何数列

公比是：

r = 0.7727272727272727

r=0.7727272727272727

该系列的和是：

s = 2925

s=2925

此系列的通用形式是：

a_{n} = 1650 \cdot {0.7727272727272727}^{n - 1}

a_n=1650*0.7727272727272727^(n-1)

这个序列的第n项是：

1650, 1275, 985.2272727272726, 761.3119834710743, 588.2865326821938, 454.5850479816952, 351.2702643494917, 271.43611336097086, 209.74608759711384, 162.07652223413342

1650,1275,985.2272727272726,761.3119834710743,588.2865326821938,454.5850479816952,351.2702643494917,271.43611336097086,209.74608759711384,162.07652223413342

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：

$a_{2} a_{1} = \frac{1275}{1650} = 0.7727272727272727$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.7727272727272727$

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： $a = 1, 650$ 、公比： $r = 0.7727272727272727$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1650 * ((1 - {0.7727272727272727}^{2}) / (1 - 0.7727272727272727))$

$s_{2} = 1650 * ((1 - 0.5971074380165289) / (1 - 0.7727272727272727))$

$s_{2} = 1650 * (0.4028925619834711 / (1 - 0.7727272727272727))$

$s_{2} = 1650 * (0.4028925619834711 / 0.2272727272727273)$

$s_{2} = 1650 \cdot 1.7727272727272727$

$s_{2} = 2925$

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： $a = 1, 650$ 和公比： $r = 0.7727272727272727$ 插入几何级数的公式：

$a_{n} = 1650 \cdot {0.7727272727272727}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1650$

$a_{2} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{2 - 1} = 1650 \cdot {0.7727272727272727}^{1} = 1650 \cdot 0.7727272727272727 = 1275$

$a_{3} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{3 - 1} = 1650 \cdot {0.7727272727272727}^{2} = 1650 \cdot 0.5971074380165289 = 985.2272727272726$

$a_{4} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{4 - 1} = 1650 \cdot {0.7727272727272727}^{3} = 1650 \cdot 0.4614012021036814 = 761.3119834710743$

$a_{5} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{5 - 1} = 1650 \cdot {0.7727272727272727}^{4} = 1650 \cdot 0.3565372925346629 = 588.2865326821938$

$a_{6} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{6 - 1} = 1650 \cdot {0.7727272727272727}^{5} = 1650 \cdot 0.27550608968587587 = 454.5850479816952$

$a_{7} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{7 - 1} = 1650 \cdot {0.7727272727272727}^{6} = 1650 \cdot 0.21289106930272225 = 351.2702643494917$

$a_{8} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{8 - 1} = 1650 \cdot {0.7727272727272727}^{7} = 1650 \cdot 0.16450673537028537 = 271.43611336097086$

$a_{9} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{9 - 1} = 1650 \cdot {0.7727272727272727}^{8} = 1650 \cdot 0.1271188409679478 = 209.74608759711384$

$a_{10} = a_{1} \cdot r^{n - 1} = 1650 \cdot {0.7727272727272727}^{10 - 1} = 1650 \cdot {0.7727272727272727}^{9} = 1650 \cdot 0.0982281952934142 = 162.07652223413342$

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几何数列