> 数学 >
若数列{xn}满足:x1=1,x2=3,且
xn+1
xn
=
3xn
xn−1
(n=2,3,4…),则它的通项xn等于 ______.
人气:223 ℃ 时间:2019-08-22 18:35:47
解答
xn+1
xn
=3
xn
xn−1
x2
x1
= 3

∴数列{
xn
xn−1
}
以3为首项,以3为公比的等比数列
xn
xn−1
3n−1

x2
x1
x3
x2
• …
xn
xn−1
31323n−1

xn
x1
31+2+…+(n−1)

xn= 3
n(n−1)
2

故答案为:3
n(n−1)
2
推荐
猜你喜欢
© 2024 79432.Com All Rights Reserved.
电脑版|手机版