数列{an}满足a1=1,a2=2,a(n+2)=(1+cos(nπ/2)^2)an+sin(nπ/2)^2,n=1,2

学习时间:2026-04-01 08:36:02 阅读：3651

数列{an}满足a1=1,a2=2,a(n+2)=(1+cos(nπ/2)^2)an+sin(nπ/2)^2,n=1,2,3,……求a3,a4,并求数列{an}的通项公式.

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2026-04-01 08:36:02

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n为奇数时 sin(nπ/2)^2=1 偶数时为0n为奇数时 1+cos(nπ/2)^2=0 偶数时为2故n为奇数时 a n+2 = 0an +1 =1n为偶数时 a n+2 = 2 an故 an = 1 (n为奇数)2^(n/2) (n为偶数)故a3=1 a4=4