In the arithmetic sequence an, a16 + A17 + A18 = A8 = - 36, find TN = | A1 | + | A2 | + · + | an| The answer is TN = {- 3 / 2 times n square + 123 / 2n, (n is less than or equal to 21, n belongs to n *) 3 / 2 times n square - 123 / 2n + 1260 (n is more than 21, n belongs to n *)*

In the arithmetic sequence an, a16 + A17 + A18 = A8 = - 36, find TN = | A1 | + | A2 | + · + | an| The answer is TN = {- 3 / 2 times n square + 123 / 2n, (n is less than or equal to 21, n belongs to n *) 3 / 2 times n square - 123 / 2n + 1260 (n is more than 21, n belongs to n *)*

a16+a17+a18=3a17=-36,∴a17=-12
Tolerance d = (a17-a9) / (17-9) = (- 12 + 36) / 8 = 3
∴an=a9+3(n-9)=3n-63
Let an0, then N21; let an0, N21
That is, A1, A2,..., A20 are all negative, A22, A23,..., a40 are all positive
Sum of two sequences (A2 +... + 3) +... (A2 +... + 3) +... - 6
=(60+3)×20/2+(3+57)×19/2=630+570=1200