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解答 - 几何数列

公比是: r=1.8181818181818181
r=1.8181818181818181
该系列的和是: s=92
s=-92
此系列的通用形式是: an=331.8181818181818181n1
a_n=-33*1.8181818181818181^(n-1)
这个序列的第n项是: 33,60,109.09090909090908,198.3471074380165,360.6311044327573,655.6929171504677,1192.1689402735776,2167.579891406505,3941.054348011827,7165.553360021503
-33,-60,-109.09090909090908,-198.3471074380165,-360.6311044327573,-655.6929171504677,-1192.1689402735776,-2167.579891406505,-3941.054348011827,-7165.553360021503

其他解决方法

几何数列

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:

a2a1=6033=1.8181818181818181

该序列的公比(r)保持不变,并且等于两个连续项的商。
r=1.8181818181818181

2. 求和

5 个额外 步骤

sn=a*((1-rn)/(1-r))

要找到系列的和,将第一项:a=33、公比:r=1.8181818181818181和元素数目n=2插入几何级数求和公式:

s2=-33*((1-1.81818181818181812)/(1-1.8181818181818181))

s2=-33*((1-3.305785123966942)/(1-1.8181818181818181))

s2=-33*(-2.305785123966942/(1-1.8181818181818181))

s2=-33*(-2.305785123966942/-0.8181818181818181)

s2=332.818181818181818

s2=92.99999999999999

3. 找到通用形式

an=arn1

要找到系列的通用形式,将第一项:a=33 和公比:r=1.8181818181818181 插入几何级数的公式:

an=331.8181818181818181n1

4. 找到第n项

使用通用公式找到第n项

a1=33

a2=a1·rn1=331.818181818181818121=331.81818181818181811=331.8181818181818181=60

a3=a1·rn1=331.818181818181818131=331.81818181818181812=333.305785123966942=109.09090909090908

a4=a1·rn1=331.818181818181818141=331.81818181818181813=336.010518407212621=198.3471074380165

a5=a1·rn1=331.818181818181818151=331.81818181818181814=3310.92821528584113=360.6311044327573

a6=a1·rn1=331.818181818181818161=331.81818181818181815=3319.86948233789296=655.6929171504677

a7=a1·rn1=331.818181818181818171=331.81818181818181816=3336.12633152344175=1192.1689402735776

a8=a1·rn1=331.818181818181818181=331.81818181818181817=3365.68423913353045=2167.579891406505

a9=a1·rn1=331.818181818181818191=331.81818181818181818=33119.42588933369173=3941.054348011827

a10=a1·rn1=331.8181818181818181101=331.81818181818181819=33217.1379806067122=7165.553360021503

为什么学习这个

几何序列常用于解释数学、物理、工程、生物、经济、计算机科学、金融等领域的概念,因此它们是我们工具箱中非常有用的工具。例如,几何序列最常见的应用之一就是计算已经获得或未付的复利,这是与金融相关的最常见活动之一,可能意味着赚取或失去大量的金钱!其他应用包括但不仅限于计算概率、测算随时间变化的放射性以及设计建筑物。

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