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Problems above mathematics
If it's a brain teaser, it may be

If it is a series of rigorous questions, then

a( 1)= 1; a(2)= 3;

a(3)=[-a( 1)-2×a(2)+ 17]/2 = 5;

a(4)=[-a(2)-2×a(3)+ 17]/2 = 2;

a(5)=[-a(3)-2×a(4)+ 17]/2 = 4 .

To sum up, the law is like this

a(n)=[-a(n-2)-2×a(n- 1)+ 17]/2 .

therefore

a(6)=[-a(4)-2×a(5)+ 17]/2 = 7/2 .

Finally found one that is not equal to 6.