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解答 - 几何数列

公比是：

r = 1.0526315789473684

r=1.0526315789473684

该系列的和是：

s = 155

s=155

此系列的通用形式是：

a_{n} = 76 \cdot {1.0526315789473684}^{n - 1}

a_n=76*1.0526315789473684^(n-1)

这个序列的第n项是：

76, 80, 84.21052631578947, 88.64265927977839, 93.30806239976671, 98.219013052386, 103.38843479198526, 108.82993135998449, 114.55782248419419, 120.58718156230965

76,80,84.21052631578947,88.64265927977839,93.30806239976671,98.219013052386,103.38843479198526,108.82993135998449,114.55782248419419,120.58718156230965

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：

$a_{2} a_{1} = \frac{80}{76} = 1.0526315789473684$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.0526315789473684$

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： $a = 76$ 、公比： $r = 1.0526315789473684$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 76 * ((1 - {1.0526315789473684}^{2}) / (1 - 1.0526315789473684))$

$s_{2} = 76 * ((1 - 1.1080332409972298) / (1 - 1.0526315789473684))$

$s_{2} = 76 * (- 0.10803324099722977 / (1 - 1.0526315789473684))$

$s_{2} = 76 * (- 0.10803324099722977 / - 0.05263157894736836)$

$s_{2} = 76 \cdot 2.052631578947368$

$s_{2} = 155.99999999999997$

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： $a = 76$ 和公比： $r = 1.0526315789473684$ 插入几何级数的公式：

$a_{n} = 76 \cdot {1.0526315789473684}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 76$

$a_{2} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{2 - 1} = 76 \cdot {1.0526315789473684}^{1} = 76 \cdot 1.0526315789473684 = 80$

$a_{3} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{3 - 1} = 76 \cdot {1.0526315789473684}^{2} = 76 \cdot 1.1080332409972298 = 84.21052631578947$

$a_{4} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{4 - 1} = 76 \cdot {1.0526315789473684}^{3} = 76 \cdot 1.166350779997084 = 88.64265927977839$

$a_{5} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{5 - 1} = 76 \cdot {1.0526315789473684}^{4} = 76 \cdot 1.2277376631548251 = 93.30806239976671$

$a_{6} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{6 - 1} = 76 \cdot {1.0526315789473684}^{5} = 76 \cdot 1.2923554348998159 = 98.219013052386$

$a_{7} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{7 - 1} = 76 \cdot {1.0526315789473684}^{6} = 76 \cdot 1.360374141999806 = 103.38843479198526$

$a_{8} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{8 - 1} = 76 \cdot {1.0526315789473684}^{7} = 76 \cdot 1.4319727810524274 = 108.82993135998449$

$a_{9} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{9 - 1} = 76 \cdot {1.0526315789473684}^{8} = 76 \cdot 1.5073397695288708 = 114.55782248419419$

$a_{10} = a_{1} \cdot r^{n - 1} = 76 \cdot {1.0526315789473684}^{10 - 1} = 76 \cdot {1.0526315789473684}^{9} = 76 \cdot 1.5866734416093375 = 120.58718156230965$

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