已知{an}满足an=2a^n-1+2^n(n≥2),其中a4=64,求a1,a2,a3,求数列的{an}的通项
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![已知{an}满足an=2a^n-1+2^n(n≥2),其中a4=64,求a1,a2,a3,求数列的{an}的通项](/uploads/image/z/15066689-41-9.jpg?t=%E5%B7%B2%E7%9F%A5%7Ban%7D%E6%BB%A1%E8%B6%B3an%3D2a%5En-1%2B2%5En%28n%E2%89%A52%29%2C%E5%85%B6%E4%B8%ADa4%3D64%2C%E6%B1%82a1%2Ca2%2Ca3%2C%E6%B1%82%E6%95%B0%E5%88%97%E7%9A%84%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9)
已知{an}满足an=2a^n-1+2^n(n≥2),其中a4=64,求a1,a2,a3,求数列的{an}的通项
已知{an}满足an=2a^n-1+2^n(n≥2),其中a4=64,求a1,a2,a3,求数列的{an}的通项
已知{an}满足an=2a^n-1+2^n(n≥2),其中a4=64,求a1,a2,a3,求数列的{an}的通项
a4=2a3+2^4=64
a3+8=32
a3=24=2a2+2^3
12=a2+4
a2=8=2a1+4
a1=2
an=2an-1+2^n
2an-1=2*2an-2+2^n
an=2*2an-2+2^(n+1)
an=2^(n-k)ak+2^(2n-k-1)
=2^(n-2)a2+2^(2n-3)
an=2^(n-2)*8+2^(2n-3) (n>=2)
a1=2
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