1、 1 3 6,11,14 1,5,8,10 2,7,9 4,12 3,13,15 ( :30 ) 1. an ,a1=,a4=-1, a6 ( A ) (A)-4 (B)4 (C)-8 (D)8 : an q, =q 3 , q=-2, a6=a1q 5 =-4. 2.(2016 ) an 1+log3an=log3an+1 (n N * ),a2+a4+a6=9, (a5+a7+a9) ( C ) (A)- (B) (C)-5 (D)5 : 1+log3an=log3an+1(n N * ), 3an=an+1, an q=3 , a5+a7+a9=q 3 (a2+a4+a6)=243, (
2、a5+a7+a9)= 243=-5. 3.(2015 ) an ,a2a10=9, a5+a7( A ) (A) 6 (B) 6 (C) 9 (D) 3 : ,an0, a2a10=9, a5a7=9. a5+a7 2 =6.( a5=a7 , ) a5+a7 6. 4.(2016 ) an ,2a3- +2a11=0, bn , b7=a7, b6b8 ( C ) (A)4 (B)2 (C)16 (D)8 : an , 2a7=a3+a11, 2a3- +2a11=0, 4a7- =0, 2 a7 0, a7=4, bn , b6b8= = =16, C. 5.(2015 ) an n Sn
3、, a1+a3=,a2+a4=, ( C ) (A)4 n -1 (B)4 n-1(C)2 n -1 (D)2 n-1 : an q, q= =, a1+a3=a1(1+q 2 )=a1(1+)=, a1=2, an=2 () n-1 =() n-2 , Sn= , = =2 n -1. 6.(2016 ) an a1=1,an+1=3Sn(n N * ), ( B ) (A) an (B) a2,a3, ,an (C) an (D) a2,a3, ,an : an+1=3Sn(n 1), an=3Sn-1(n 2), an+1-an=3an(n 2), an+1=4an(n 2), a1=1
4、,an+1=3Sn(n 1), a2=3, a2,a3, ,an 4 . 7. an a1=-1, n Sn, = , an an= . : = , =- , 3 S5,S10-S5,S15-S10 , q 5 , q 5 =- ,q=-, an=-1 - n-1 =- n-1 . :- (-) n-18. an , a2 a6=9a4,a2=1, a1= . : a2 a6=9a4 a2(a2q 4 )=9a2q 2 , q 2 =9, q=3 q=-3( ), a2=a1q, a1=. : 9.(2016 ) an q, n Tn, a11,a99a100-10, 1 n 198, . :
5、 (a99-1)(a100-1)1,a99a1001, a991,01,T199=a1a2 a199=(a1a199)(a2a198) (a99a101)a1000, S3-3a1-2a2=0, a1+a2+a3-3a1-2a2=0, a3-2a1-a2=0, a1q 2 -2a1-a1q=0, a1 q=2 q=-1( ), an,am =4a1, aman=16 , 5 q m+n-2 =16 , q m+n-2 =16, 2 m+n-2 =16, m+n-2=4, (m+n)=1, +=(+)(m+n)= (5+ ) (5+2 )=, = , m=2 n=4 , + . 14.(2014
6、 ) an n Sn= ,n N * . (1) an ; (2) : n1, m N * , a1,an,am . (1) : Sn= , a1=S1=1, n 2 ,an=Sn-Sn-1=3n-2, an :an=3n-2. (2) : a1,an,am , =a1 am, (3n-2) 2 =1 (3m-2), m=3n 2 -4n+2, m N * , mn. n1, m N * , a1,an,am . 15.(2015 ) an , n Sn, a3=,S3=, (1) an ; (2) n, Sn-Sn+2= , , n , , . :(1) q, , a1q 2 =,a1+a1
7、q+a1q 2 =, a1=,q=1 a1=6,q=-, an an= an=6 (-) n-1 . (2) n, Sn-Sn+2= , 6 a1=,q=1 , Sn-Sn+2= n-(n+2)= , ; a1=6,q=- , Sn=41-(-) n , Sn-Sn+2= (-) n =- n=5. , n=5, Sn-Sn+2= . 5 1.(2015 ) a,b,c , a+b+c=1 , b ( D ) (A)(0, (B)-1, (C)-,0) (D)-1,0) (0, : a,c b q , a+b+c=1 b q , . : a,b,c , ,b,bq, a+b+a=1 , +b+bq=1, b= = , q+ (- ,-2 2,+ ), b -1,0) (0,. 2.(2015 ) y= , ( D ) (A) (B) (C) (D) : , . : y= (5,0), 3 ( ), 2( (2,0) ), 8( (8,0) ), 7 , q 8=2q 2 , q 2 =4,q=2, 2=8q 2 , q 2 =, q=. , q 1, q 2, q 1.
