a1=1 a（n+1)=2/3an+1 求an
a1=1 a（n+1)=2/3an+1 求an
數(shù)學(xué)人氣：980 ℃時(shí)間：2020-10-01 21:31:55
優(yōu)質(zhì)解答
a(n+1)=(2/3)an+1 ∴a(n+1)-3=(2/3)an+1-3=(2/3)an-2=(2/3)(an-3),a1-3=1-3=-2 ∴{an-3}是首項(xiàng)為-2,公比為(2/3)的等比數(shù)列 ∴an-3=-2×(2/3)^(n-1)=-3×(2/3)×(2/3)^(n-1)=-3×(2/3)^n ∴an=3-3×(2/3)^n
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