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Leading to mathematics
Solution:

Meaning: a1=12-8×1=-7.

According to the condition sn = n 2-8n ...

s(n- 1)=(n- 1)^2-8(n- 1)…②

①-②: sn-s(n- 1)=2n-9。

By an=sn-s(n- 1)

So an=2n-9, and this formula applies to a 1.

So the general formula of {an} is 2n-9.

N is an integer, 2n-9 < 0 when n≤4, and 2n-9 > 0 when n≥5.

Therefore, the general formula of {|an|}

When n≤4, |an|=9-2n.

When n≥5, | an | = 2n-9;

(2)

When n≤4

Every term is negative, so add a negative sign to remove the absolute value.

So pn = 8n-n 2 (n ≤ 4).

When n≥5,

Because S4 = a1+A2+A3+A4 = |-7 |+|-5 |+|-kloc-0/| =16.

Therefore, pn = S4+[1+3+...+(2n-9)] = (1+2n-9) (n-4)/2+16 = n 2-8n+32.

Therefore, when n≤4, pn = 8n-n 2.

When n≥5, pn = n 2-8n+32.