1、 1 2017 6.3 n 60 an an an 2an 1 n 2,3,4 an 2 ( ) A B C D C an an 1 2 n 2,3,4 q 2 C. 2 an a1 3 a4 24 a3 a4 a5 ( ) A 33 B 72 C 84 D 189 C q 3 8 q 2. a3 a4 a5 a1q 2 (1 q q 2 ) 84. 3 an n Sn Sm 1 5 Sm 11 Sm 1 21 m ( ) A 3 B 4 C 5 D 6 C Sm Sm 1 am 16 Sm 1 Sm am 1 32 q am 1 am 2 Sm a1 amq 1 q 11 a1 1 am a
2、1 q m 1 16 ( 2) m 1 16 m 5. an a5a6 a4a7 18 log3a1 log3a2 log3a10 ( ) A 12 B 10 C 8 D 2 log35 B a5a6 a4a7 a5a6 a4a7 18 a5a6 a4a7 9 log3a1 log3a2 log3a10 log3(a1 a2 a10) log3(a5a6) 5 log3 9 5 log33 10 10. 5 an an0 n 1,2 a5 a2n 5 2 2n (n log2a1 log2a3 log2a2n 1 ( ) 2 A n(2n 1) B (n 1) 2C n 2D (n 1) 2
3、C a5 a2n 5 a1 a2n 1 2 2n . log2a1 log2a3 log2a2n 1 log2(a1 a3 a2n 1) a1 a3 a2n 1 (a1 a2n 1) n 2 (2 2n ) n 2 2n 2 log2a1 log2a3 log2a2n 1 n 2 . 6 an n Sn Sn 2 S3n 14 S4n ( ) A 80 B 30 C 26 D 16 B Sn S2n Sn S3n S2n S4n S3n S2n x 2 x 2,14 x (x 2) 2 x) x 6 x 4( ) S2n 6.Sn S2n Sn S3n S2n S4n S3n 2 2 S3n
4、14 S4n 14 3 30 B. 7 0 an a1 a3 a9 Sn an n S11 S9 S7 S6 _. 3 d (a1 2d) 2 a1(a1 8d) a1d d 2 d a1 d S11 S9 S7 S6 66a1 45a1 28a1 21a1 3. 8 an a1 1 an 1 1 2 an(n N * ) n Sn S4 a4 _. 15 a1 1 an 1 1 2 an an 1 1 2 S4 1 1 2 4 1 1 2 15 8 a4 a1q 3 1 8 S4 a4 15. 9 an am 3 4 amam 4 a 2 4(m N * m4) a1a5 _ 16 3 an
5、 q amam 4 a 2 4 m (m 4) m 6 am 3 4 a3 4 a1a5 a 2 3 16. 10 2 an a2 a5 a8 a11 a14 a17 a20 13 21 S21 _. 91 2 a1 q 2, n Sn. a2 a5 a8 a11 a14 a17 a20 a2 q 3 7 T7 a21 q 3 7 1 q 3 a1q q 21 q q q 2 a1 q 21 1 q q 1 q q 2 S21 2 7 13 S21 91 2 . 11 an 2a1 a2 a3,3a6 8a1a3. (1) an (2) bn log2a1 log2a2 log2an nlog
6、23 1 bn 1 n Tn. (1) an q a10 q0 2a1 a1q a1q 2 3a1q 5 8a 2 1q 2 a1 3 q 2 an n 1 (n N * ) (2) log2an log23 n 1 log2a1 log23 log2an log23 1 bn log23 log23 n 1 2 n nlog23 n n 2 . Tn 1 b2 1 b3 1 b4 1 bn 1 2 2 2 2 n n 2 1 1 1 2 2 1 2 1 3 2 1 n 1 n 1 2 1 1 n 1 2n n 1 . 12 a0 a2a4 a 2 1q 4 1 S3 a1 a1q a1q 2
7、 7 q 1 2 1 3 ( ) a1 4 S5 a1 q 5 1 q 1 1 32 1 1 2 31 4 . 14 an a1 1 bn bn an 1 an b10b11 2015 1 10 a21 _. 2015 bn an 1 an a1 1 b1 a2 a1 a2 b2 a3 a2 a3 a2b2 b1b2 b3 a4 a3 a4 a3b3 b1b2b3 bn 1 an an 1 an b1b2 bn 1 a21 b1b2 b20. bn a21 (b1b20)(b2b19 b10b11) (b10b11) 10 (2015 1 10 ) 10 2015. 15 0 an n Sn
8、S3 a4 6 a1 a4 a13 (1) an (2) bn 2an 1 bn n (1) an d(d S3 a4 6 3a1 d 2 a1 3d 6. a1 3. a1 a4 a13 a1(a1 12d) (a1 3d) 2 3(3 12d) (3 3d) 2 . d 2. an 2n 1. 5 (2) bn 2 2n 1 1 bn n Tn cn 2 2n 1 cn 1 cn 2 n 1 2 2n 1 4(n N * ) cn 8 4 Tn 4 n 1 4 n 2 2n 3 8 3 n. an a1 1 an 1 2 1 1 n 2 an. (1) bn an n 2 bn (2) an (3) cn an 1 2an cn n Sn. (1) an 1 n 2 n 2 an an 1 n 2 an n 2 bn 1 2bn bn 2 (2) (1) bn 2 b1 a1 1 2 a1 1 bn b1 n 1 2 n 1 an n 2 2 n 1 an n 2 n 1 . (3)cn (n 1) 2 n 2n 2 n 1 (2n 2 n Sn 2 3 (2n n . 2Sn 2 3 (2n n (2n n 1 . Sn 2 3 n (2n n 1 2 2 n 1 2 (2n n 1 2 (2n n 1 Sn (2n n 1 2.
