It is known that {an} is an arithmetic sequence. If a1 + A5 + A9 = 8 π, then the value of COS (A2 + A8) is______ ．

It is known that {an} is an arithmetic sequence. If a1 + A5 + A9 = 8 π, then the value of COS (A2 + A8) is______ ．

Let the tolerance of arithmetic sequence be D, ∵ {an} be arithmetic sequence, a1 + A5 + A9 = 8 π, ∵ 3A1 + 12D = 8 π, ∵ A2 + A8 = 2A1 + 8D = 2 (a1 + 4D) = 2.8 π 3 = 16 π 3, ∵ cos (A2 + A8) = cos16 π 3 = Cos2 π 3 = - 12

In the arithmetic sequence {an}, if the sum of the first four items is 1 and the sum of the first eight items is 4, then A17 + A18 + A19 + A20=______ ．

In ∵ arithmetic sequence {an}, the first four terms and S4 = a1 + A2 + a3 + A4 = 1, the first eight terms and S8 = 4; ∵ s8-s4 = A5 + A6 + A7 + A8 = (a1 + 4D) + (A2 + 4D) + (A3 + 4D) + (A4 + 4D) = S4 + 16d = 1 + 16d = 4-1, ∵ 16d = 2; ∵ A17 + A18 + A19 + A20 = (a1 + 16d) + (A2 + 16d) + (A3 + 6D) + (A4 + 16

In the arithmetic sequence {an}, if S4 = 1, S8 = 4, then the value of A17 + A18 + A19 + A20 is ()
A. 9B. 12C. 16D. 17

Let the first term be A1 and the tolerance be d. from Sn = Na1 + n (n − 1) D2, S4 = 4A1 + 6D = 1, S8 = 8A1 + 28d = 4, and the solution is A1 = 116, d = 18. So A17 + A18 + A19 + A20 = s20-s16 = 4A1 + 70D = 4 × 116 + 70 × 18 = 9