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解答 - 几何数列

公比是：

r = 0.06832298136645963

r=0.06832298136645963

该系列的和是：

s = 344

s=344

此系列的通用形式是：

a_{n} = 322 \cdot {0.06832298136645963}^{n - 1}

a_n=322*0.06832298136645963^(n-1)

这个序列的第n项是：

322, 22, 1.503105590062112, 0.10269665522163499, 0.007016541661105497, 0.00047939104516869855, 3.27534254463086 E - 05, 2.2378116764558668 E - 06, 1.5289396547214 E - 07, 1.0446171553997144 E - 08

322,22,1.503105590062112,0.10269665522163499,0.007016541661105497,0.00047939104516869855,3.27534254463086E-05,2.2378116764558668E-06,1.5289396547214E-07,1.0446171553997144E-08

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：

$a_{2} a_{1} = \frac{22}{322} = 0.06832298136645963$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.06832298136645963$

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： $a = 322$ 、公比： $r = 0.06832298136645963$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 322 * ((1 - {0.06832298136645963}^{2}) / (1 - 0.06832298136645963))$

$s_{2} = 322 * ((1 - 0.00466802978280159) / (1 - 0.06832298136645963))$

$s_{2} = 322 * (0.9953319702171984 / (1 - 0.06832298136645963))$

$s_{2} = 322 * (0.9953319702171984 / 0.9316770186335404)$

$s_{2} = 322 \cdot 1.0683229813664596$

$s_{2} = 344$

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： $a = 322$ 和公比： $r = 0.06832298136645963$ 插入几何级数的公式：

$a_{n} = 322 \cdot {0.06832298136645963}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 322$

$a_{2} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{2 - 1} = 322 \cdot {0.06832298136645963}^{1} = 322 \cdot 0.06832298136645963 = 22$

$a_{3} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{3 - 1} = 322 \cdot {0.06832298136645963}^{2} = 322 \cdot 0.00466802978280159 = 1.503105590062112$

$a_{4} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{4 - 1} = 322 \cdot {0.06832298136645963}^{3} = 322 \cdot 0.00031893371186843164 = 0.10269665522163499$

$a_{5} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{5 - 1} = 322 \cdot {0.06832298136645963}^{4} = 322 \cdot 2.179050205312266 E - 05 = 0.007016541661105497$

$a_{6} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{6 - 1} = 322 \cdot {0.06832298136645963}^{5} = 322 \cdot 1.4887920657413 E - 06 = 0.00047939104516869855$

$a_{7} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{7 - 1} = 322 \cdot {0.06832298136645963}^{6} = 322 \cdot 1.0171871256617577 E - 07 = 3.27534254463086 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{8 - 1} = 322 \cdot {0.06832298136645963}^{7} = 322 \cdot 6.94972570327909 E - 09 = 2.2378116764558668 E - 06$

$a_{9} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{9 - 1} = 322 \cdot {0.06832298136645963}^{8} = 322 \cdot 4.748259797271429 E - 10 = 1.5289396547214 E - 07$

$a_{10} = a_{1} \cdot r^{n - 1} = 322 \cdot {0.06832298136645963}^{10 - 1} = 322 \cdot {0.06832298136645963}^{9} = 322 \cdot 3.244152656520852 E - 11 = 1.0446171553997144 E - 08$

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几何数列