1、 1 2 13,14 1,3,10 2,4,8,9 5,7,12 6,11,15 ( :30 ) 1.(2016 ) Sn an n , a3=3,S9-S6=27, a1 ( D ) (A)- (B)- (C) (D) : a1=. D. 2.(2015 ) an , a1+a7+a13=4, a2+a12 ( B ) (A) (B) (C)2 (D)4 : a1+a7+a13=3a7=4, a7=. a2+a12=2a7=2 =. 3.(2016 ) Sn an n , =, ( D ) (A) (B) (C)4 (D)5 : =, =, a1=-. = = = =5. 4.(2015 )
2、 an , n Sn, a1a2a3=10, =, a2 ( A ) (A)2 (B)3 (C)4 (D)5 : S5= =5a3, =, 2 =, a1a3=5, a1a2a3=10, a2=2. 5. an n Sn, a2=-9, a3+a7=-6, Sn ,n ( D ) (A)9 (B)8 (C)7 (D)6 : a3+a7=2a5=-6, a5=-3, d=2, a6=-1,a7=1, S6 . D. 6.(2015 ) an . ( C ) (A) a1+a20, a2+a30 (B) a1+a3 (D) a10 : an , 2a2=a1+a3. a2a10 , d0, a30
3、, a1+a32 , 2a22 , a2 , C. 7.(2016 ) an , n Sn, 1+ 0 n . : Sn , an . 0,a110, S20=20 =10(a10+a11)1,n N * ). (1) a1,a2 an; (2) Sn an n , S1,S2,S3, ? :(1) an a3=-13,an=an-1+4, an-an-1=4, an d=4, a2=a3-d=-13-4=-17, a1=a2-d=-17-4=-21, an=a1+(n-1)d=-21+4(n-1)=4n-25. 4 (2) an=4n-25 0 n , an 6 , 7 , S1,S2,S3
4、, S6 . ( :15 ) 12.(2015 ) an n Sn, S170,S180, a90, S18=9(a1+a18)=9(a9+a10)0,0, ,0, a2 a9, , , . 13. an :a1=1,a2=2,2 = + (n N * ,n 2), a7= . : 2 = + (n N * ,n 2), =1 , d= - =4-1=3 , =1+3(n-1)=3n-2, an= ,n 1. a7= = . : 14. a,4,3a, n Sn, Sk=110. (1) a k ; (2) bn bn=, bn , n Tn. :(1) an, 5 a1=a,a2=4,a3=
5、3a, a+3a=8, a1=a=2, d=4-2=2, Sk=ka1+ d=2k+ 2=k 2 +k. Sk=110, k 2 +k-110=0, k=10 k=-11( ), a=2,k=10. (2) (1) Sn= =n(n+1), bn=n+1, bn+1-bn=(n+2) -(n+1)=1, bn 2, 1 , Tn= = . 15.(2015 ) an a1=1,an= (n N * ,n 2), bn bn=(n N * ). (1) : bn ; (2) an . (1) : bn=, an= , bn+1= = = . bn+1-bn= -=2. b1=1, bn 1, 2
6、 . (2) : (1) bn bn=1+(n-1) 2=2n-1, bn=, an= . an an= . 6 5 1.(2015 ) f(x)=x 2 -2x+4, an d , a1=f(d-1),a3=f(d+1), an ( B ) (A)an=2n-2 (B)an=2n+1 (C)an=2n+3 (D)an=n+2 : d. : f(x)=x 2 -2x+4, a1=f(d-1)=(d-1) 2 -2(d-1)+4=d 2 -4d+7, a3=f(d+1)=(d+1) 2 -2(d+1)+4=d 2 +3, a3-a1=4d-4, 2d=4d-4, d=2, a1=3, an=3+2(n-1)=2n+1. 2. an a3=3,a6=-3, an n Sn . : a1 d, Sn=An 2 +Bn , . : a3=3,a6=-3 , Sn=na1+ d=-n 2 +8n=-(n-4) 2 +16. n=4 Sn 16. a3=3,a6=-3 an=9-2n. n 4 ,an0, n 5 ,an0, 4 S4=4 7+ (-2)=16. :16
