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

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

In the arithmetic sequence, if S4 = 1, S8 = 4, then A17 + A18 + A19 + A20 =?

In the arithmetic sequence, SK, S2K SK, s3k-s2k,. Also form the arithmetic sequence,
So S4, s8-s4, s12-s8, s16-s12, s20-s16 are equal difference series, set as B1, B2, B3, B4, B5,
B1 = 1, B2 = 3, tolerance d '= 2, B5 = B1 + (5-1) d' = 1 + 4 * 2 = 9,
That is, A17 + A18 + A19 + A20 = 9

(1) In the arithmetic sequence an, S4 = 1, S8 = 4, then the sum of the first n terms of A17 + A18 + A19 + A20 = (2) arithmetic sequence-2,1,4 is
(3) If the arithmetic sequence A1 = 2, A2 + a3 = 13, then A4 + A5 + A6=

(1) Because S4 = 1, S8 = 4, so s8-s4 = 4-1 = 3, because S4, s8-s4, s12-s8, s16-s12, s20-s16. Are also arithmetic series, so s20-s16 = S4 + 4 * d = 1 + 4 * (3-1) = 9, that is, A17 + A18 + A19 + A20 = s20-s16 = 9. Note: it can also be done by conventional method, but it is troublesome. (2) the first item is A1 = - 2, and the tolerance is d = 4-1 =