齐鲁名校联盟2023—2024学年（下）高三年级开学质量检测数学·答案一、单项选择题：本题共8小题，每小题5分，共40分l.C2.B3.B4.D5.86.A7.C8.D二、多项选择题：本题共3小题，每小题6分，共18分．每小题全部选对的得6分，部分选对的得部分分，有选错的得0分9.AD10.BC11.ACD三、填空题：本题共3小题，每小题5分，共15分．12.413.0.9514.土2四、解答题：本题共5小题，共77分解答应写出文字说明、证明过程或演算步骤．15．解析(I)因为nan+i=2Sn+3n,所以当n立时，（n-l)an=2Sn-l+3(n-1),.................................................................................分）两式相减，得nan+i-(n+l)an=3,心(2所以(n+l)an+2-(n+2)an+l=3,(2)＠－心，得(n+l)an+2+(n+l)an=(2n+2)an+1,:;::,,..........................................................................................分）所以an+2+an=2an+l(n2).(4当n=l时，a2=2S1+3=2a1+3=9,当n=2时，2a3=2S2+6=24+6=30,a3=15............................................................................分）所以a3+a1=2a2，所以an+2+an=2an+)•(6(II)由(I)知Ian}是首项为3，公差为6的等差数列，.......................................................................................所以a几＝3+6(n-1)=6n-3,(8分）an2n-1.........................................................................................................分）b_n=+l=�,＇(93n3九1352n-1———＋.．．＋所以兀＝＋2'+3''3•'33332分辛扣n十t+＋＋;卫，2122222n-1两式相减，得—T=—+—+—+—+.．．+—-3~n3,32,33,343n3n+l2�=++-�=++-½-(1-fi)-�=于－2；了，．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．（l1分）l-—3n+l所以T=l-�.......................................................................................................(13分）n3n•—l—{#{QQABLQwUggCAQhAAAQgCQwE4CAKQkBECCIoOQBAEIAAAyAFABAA=}#}{#{QQABLQwUggCAQhAAAQgCQwE4CAKQkBECCIoOQBAEIAAAyAFABAA=}#}{#{QQABLQwUggCAQhAAAQgCQwE4CAKQkBECCIoOQBAEIAAAyAFABAA=}#}{#{QQABLQwUggCAQhAAAQgCQwE4CAKQkBECCIoOQBAEIAAAyAFABAA=}#}{#{QQABLQwUggCAQhAAAQgCQwE4CAKQkBECCIoOQBAEIAAAyAFABAA=}#}