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解答 - 几何数列

公比是：

r = 1.0303030303030303

r=1.0303030303030303

该系列的和是：

s = 67

s=67

此系列的通用形式是：

a_{n} = 33 \cdot {1.0303030303030303}^{n - 1}

a_n=33*1.0303030303030303^(n-1)

这个序列的第n项是：

33, 34, 35.03030303030303, 36.09182736455464, 37.18551910287447, 38.312353015082785, 39.47333340947924, 40.6694950279483, 41.90190396818915, 43.17165863389186

33,34,35.03030303030303,36.09182736455464,37.18551910287447,38.312353015082785,39.47333340947924,40.6694950279483,41.90190396818915,43.17165863389186

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：

$a_{2} a_{1} = \frac{34}{33} = 1.0303030303030303$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.0303030303030303$

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： $a = 33$ 、公比： $r = 1.0303030303030303$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 33 * ((1 - {1.0303030303030303}^{2}) / (1 - 1.0303030303030303))$

$s_{2} = 33 * ((1 - 1.061524334251607) / (1 - 1.0303030303030303))$

$s_{2} = 33 * (- 0.06152433425160697 / (1 - 1.0303030303030303))$

$s_{2} = 33 * (- 0.06152433425160697 / - 0.030303030303030276)$

$s_{2} = 33 \cdot 2.030303030303032$

$s_{2} = 67.00000000000006$

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： $a = 33$ 和公比： $r = 1.0303030303030303$ 插入几何级数的公式：

$a_{n} = 33 \cdot {1.0303030303030303}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 33$

$a_{2} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{2 - 1} = 33 \cdot {1.0303030303030303}^{1} = 33 \cdot 1.0303030303030303 = 34$

$a_{3} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{3 - 1} = 33 \cdot {1.0303030303030303}^{2} = 33 \cdot 1.061524334251607 = 35.03030303030303$

$a_{4} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{4 - 1} = 33 \cdot {1.0303030303030303}^{3} = 33 \cdot 1.0936917383198375 = 36.09182736455464$

$a_{5} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{5 - 1} = 33 \cdot {1.0303030303030303}^{4} = 33 \cdot 1.1268339122083173 = 37.18551910287447$

$a_{6} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{6 - 1} = 33 \cdot {1.0303030303030303}^{5} = 33 \cdot 1.160980394396448 = 38.312353015082785$

$a_{7} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{7 - 1} = 33 \cdot {1.0303030303030303}^{6} = 33 \cdot 1.1961616184690678 = 39.47333340947924$

$a_{8} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{8 - 1} = 33 \cdot {1.0303030303030303}^{7} = 33 \cdot 1.2324089402408576 = 40.6694950279483$

$a_{9} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{9 - 1} = 33 \cdot {1.0303030303030303}^{8} = 33 \cdot 1.2697546657027017 = 41.90190396818915$

$a_{10} = a_{1} \cdot r^{n - 1} = 33 \cdot {1.0303030303030303}^{10 - 1} = 33 \cdot {1.0303030303030303}^{9} = 33 \cdot 1.3082320798149047 = 43.17165863389186$

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