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解答 - 几何数列

公比是：

r = 0.01572722697533971

r=0.01572722697533971

该系列的和是：

s = 8073

s=8073

此系列的通用形式是：

a_{n} = 7948 \cdot {0.01572722697533971}^{n - 1}

a_n=7948*0.01572722697533971^(n-1)

这个序列的第n项是：

7948, 125, 1.9659033719174637, 0.030918208541731627, 0.00048625768340670024, 7.647484955440051 E - 06, 1.2027373168470137 E - 07, 1.8915722773764057 E - 09, 2.974918654655897 E - 11, 4.678722091494554 E - 13

7948,125,1.9659033719174637,0.030918208541731627,0.00048625768340670024,7.647484955440051E-06,1.2027373168470137E-07,1.8915722773764057E-09,2.974918654655897E-11,4.678722091494554E-13

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：

$a_{2} a_{1} = \frac{125}{7948} = 0.01572722697533971$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.01572722697533971$

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： $a = 7, 948$ 、公比： $r = 0.01572722697533971$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 7948 * ((1 - {0.01572722697533971}^{2}) / (1 - 0.01572722697533971))$

$s_{2} = 7948 * ((1 - 0.000247345668333853) / (1 - 0.01572722697533971))$

$s_{2} = 7948 * (0.9997526543316662 / (1 - 0.01572722697533971))$

$s_{2} = 7948 * (0.9997526543316662 / 0.9842727730246603)$

$s_{2} = 7948 \cdot 1.0157272269753397$

$s_{2} = 8073$

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： $a = 7, 948$ 和公比： $r = 0.01572722697533971$ 插入几何级数的公式：

$a_{n} = 7948 \cdot {0.01572722697533971}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 7948$

$a_{2} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{2 - 1} = 7948 \cdot {0.01572722697533971}^{1} = 7948 \cdot 0.01572722697533971 = 125$

$a_{3} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{3 - 1} = 7948 \cdot {0.01572722697533971}^{2} = 7948 \cdot 0.000247345668333853 = 1.9659033719174637$

$a_{4} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{4 - 1} = 7948 \cdot {0.01572722697533971}^{3} = 7948 \cdot 3.890061467253602 E - 06 = 0.030918208541731627$

$a_{5} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{5 - 1} = 7948 \cdot {0.01572722697533971}^{4} = 7948 \cdot 6.117987964352041 E - 08 = 0.00048625768340670024$

$a_{6} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{6 - 1} = 7948 \cdot {0.01572722697533971}^{5} = 7948 \cdot 9.62189853477611 E - 10 = 7.647484955440051 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{7 - 1} = 7948 \cdot {0.01572722697533971}^{6} = 7948 \cdot 1.5132578219011246 E - 11 = 1.2027373168470137 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{8 - 1} = 7948 \cdot {0.01572722697533971}^{7} = 7948 \cdot 2.379934923724718 E - 13 = 1.8915722773764057 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{9 - 1} = 7948 \cdot {0.01572722697533971}^{8} = 7948 \cdot 3.7429776731956435 E - 15 = 2.974918654655897 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = 7948 \cdot {0.01572722697533971}^{10 - 1} = 7948 \cdot {0.01572722697533971}^{9} = 7948 \cdot 5.886665942997678 E - 17 = 4.678722091494554 E - 13$

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几何数列