令bn=log3(an)
则
b(n+1)=log3(2)+n+5bn
b(n+1)+x(n+1)+y=log3(2)+n+x(n+1)+y+5bn
b(n+1)+x(n+1)+y=5[bn+(x+1)/5*n+1/5*log3(2)++1/5x++1/5y]
令x=(x+1)/5
y=1/5*log3(2)++1/5x++1/5y
所以
x=1/4
y=1/4*log3(2)+1/16
所以
b(n+1)+(n+1)/4+1/4*log3(2)+1/16=5[bn+1/4*n+1/4*log3(2)+1/16]
所以数列bn+1/4*n+1/4*log3(2)+1/16是等比数列，q=5
b1=log3(7)
则bn+1/4*n+1/4*log3(2)+1/16=[log3(7)+1/4*log3(2)+5/16]*5^(n-1)
所以bn=[log3(7)+1/4*log3(2)+5/16]*5^(n-1)-1/4*n-1/4*log3(2)-1/16
an=3^(bn)
自己整理一下吧
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