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解答 - 几何数列

公比是：

r = 7.363636363636363

r=7.363636363636363

该系列的和是：

s = 92

s=92

此系列的通用形式是：

a_{n} = 11 \cdot {7.363636363636363}^{n - 1}

a_n=11*7.363636363636363^(n-1)

这个序列的第n项是：

11, 81, 596.4545454545455, 4392.074380165289, 32341.63861758076, 238152.06618400378, 1753665.214627664, 12913352.944076436, 95089235.31547192, 700202550.9593842

11,81,596.4545454545455,4392.074380165289,32341.63861758076,238152.06618400378,1753665.214627664,12913352.944076436,95089235.31547192,700202550.9593842

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：

$a_{2} a_{1} = \frac{81}{11} = 7.363636363636363$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 7.363636363636363$

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： $a = 11$ 、公比： $r = 7.363636363636363$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 11 * ((1 - {7.363636363636363}^{2}) / (1 - 7.363636363636363))$

$s_{2} = 11 * ((1 - 54.22314049586777) / (1 - 7.363636363636363))$

$s_{2} = 11 * (- 53.22314049586777 / (1 - 7.363636363636363))$

$s_{2} = 11 * (- 53.22314049586777 / - 6.363636363636363)$

$s_{2} = 11 \cdot 8.363636363636363$

$s_{2} = 92$

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： $a = 11$ 和公比： $r = 7.363636363636363$ 插入几何级数的公式：

$a_{n} = 11 \cdot {7.363636363636363}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 11$

$a_{2} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{2 - 1} = 11 \cdot {7.363636363636363}^{1} = 11 \cdot 7.363636363636363 = 81$

$a_{3} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{3 - 1} = 11 \cdot {7.363636363636363}^{2} = 11 \cdot 54.22314049586777 = 596.4545454545455$

$a_{4} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{4 - 1} = 11 \cdot {7.363636363636363}^{3} = 11 \cdot 399.27948910593534 = 4392.074380165289$

$a_{5} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{5 - 1} = 11 \cdot {7.363636363636363}^{4} = 11 \cdot 2940.1489652346145 = 32341.63861758076$

$a_{6} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{6 - 1} = 11 \cdot {7.363636363636363}^{5} = 11 \cdot 21650.187834909433 = 238152.06618400378$

$a_{7} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{7 - 1} = 11 \cdot {7.363636363636363}^{6} = 11 \cdot 159424.11042069673 = 1753665.214627664$

$a_{8} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{8 - 1} = 11 \cdot {7.363636363636363}^{7} = 11 \cdot 1173941.1767342214 = 12913352.944076436$

$a_{9} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{9 - 1} = 11 \cdot {7.363636363636363}^{8} = 11 \cdot 8644475.937770175 = 95089235.31547192$

$a_{10} = a_{1} \cdot r^{n - 1} = 11 \cdot {7.363636363636363}^{10 - 1} = 11 \cdot {7.363636363636363}^{9} = 11 \cdot 63654777.359944016 = 700202550.9593842$

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