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解答 - 几何数列

公比是：

r = 3.3846153846153846

r=3.3846153846153846

该系列的和是：

s = 114

s=114

此系列的通用形式是：

a_{n} = 26 \cdot {3.3846153846153846}^{n - 1}

a_n=26*3.3846153846153846^(n-1)

这个序列的第n项是：

26, 88, 297.84615384615387, 1008.094674556213, 3412.0127446517977, 11548.350828052238, 39086.72587956142, 132293.5337462079, 447762.72960254975, 1515504.6232701684

26,88,297.84615384615387,1008.094674556213,3412.0127446517977,11548.350828052238,39086.72587956142,132293.5337462079,447762.72960254975,1515504.6232701684

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：

$a_{2} a_{1} = \frac{88}{26} = 3.3846153846153846$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 3.3846153846153846$

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： $a = 26$ 、公比： $r = 3.3846153846153846$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 26 * ((1 - {3.3846153846153846}^{2}) / (1 - 3.3846153846153846))$

$s_{2} = 26 * ((1 - 11.455621301775148) / (1 - 3.3846153846153846))$

$s_{2} = 26 * (- 10.455621301775148 / (1 - 3.3846153846153846))$

$s_{2} = 26 * (- 10.455621301775148 / - 2.3846153846153846)$

$s_{2} = 26 \cdot 4.384615384615385$

$s_{2} = 114.00000000000001$

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： $a = 26$ 和公比： $r = 3.3846153846153846$ 插入几何级数的公式：

$a_{n} = 26 \cdot {3.3846153846153846}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 26$

$a_{2} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{2 - 1} = 26 \cdot {3.3846153846153846}^{1} = 26 \cdot 3.3846153846153846 = 88$

$a_{3} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{3 - 1} = 26 \cdot {3.3846153846153846}^{2} = 26 \cdot 11.455621301775148 = 297.84615384615387$

$a_{4} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{4 - 1} = 26 \cdot {3.3846153846153846}^{3} = 26 \cdot 38.77287209831589 = 1008.094674556213$

$a_{5} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{5 - 1} = 26 \cdot {3.3846153846153846}^{4} = 26 \cdot 131.23125940968453 = 3412.0127446517977$

$a_{6} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{6 - 1} = 26 \cdot {3.3846153846153846}^{5} = 26 \cdot 444.1673395404707 = 11548.350828052238$

$a_{7} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{7 - 1} = 26 \cdot {3.3846153846153846}^{6} = 26 \cdot 1503.3356107523623 = 39086.72587956142$

$a_{8} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{8 - 1} = 26 \cdot {3.3846153846153846}^{7} = 26 \cdot 5088.212836392611 = 132293.5337462079$

$a_{9} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{9 - 1} = 26 \cdot {3.3846153846153846}^{8} = 26 \cdot 17221.643446251914 = 447762.72960254975$

$a_{10} = a_{1} \cdot r^{n - 1} = 26 \cdot {3.3846153846153846}^{10 - 1} = 26 \cdot {3.3846153846153846}^{9} = 26 \cdot 58288.63935654494 = 1515504.6232701684$

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