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N problems and exercises before mathematics
The solution is sn =-n 2+9 n.

When n≥2, Sn =-(n- 1) 2+9 (n- 1).

Subtract the two expressions to get An=-2n+ 10(n≥2).

When n= 1, a 1=S 1=- 1? +9=8 applies to =-2n+ 10.

That is the general formula of the sequence {an} an=-2n+ 10.

Let an≥0, that is, n≤5, that is, bn=an=-2n+ 10.

That is, an < 0, that is, n > 5, that is, bn=-an=2n- 10.

Therefore, when n≤5, sn = b1+B2+...+bn = n/2 (b1+bn) = n/2 (8-2n+10) = n/2 (/kloc-0).

When n > 5, Sn = b1+B2+B3+B4+B5+B6+B7+...+BN.

=(b 1+B2+B3+B4+b5)+(B6+B7+....+bn)

=5*(9-5)+(n-5)/2(b6+bn)

=5*(9-5)+(n-5)/2(2+2n- 10)

=20+(n-5)(n-4)

=n? -9n+40