Mathematical Problem: Identifying Arithmetic and Geometric Sequences, Exercises of Mathematics

Download Mathematical Problem: Identifying Arithmetic and Geometric Sequences and more Exercises Mathematics in PDF only on Docsity! Tu duy mé tréc nghiém toan ly 168 CAU VAN DUNG CAO CSC - CSN Suu tam va tong hop Mén: Toan (Dé thi c6 16 trang) 168 cau trac nghiém Cau 1. Cho bén sé thuc a, b, c, d 1a bén sé hang lién tiép cia mot cAp s6 cong. Biét tong cia ching bang 4 va tong cdc binh phugng cia ching bang 24. Tinh P= a9 +09 + +43. @P=79. ® P=16. © P=20. Op =64. Cau 2. Day sé (u,) xdc dinh béi u, = 3n — 2, véi n > 1. Tinh tong $ = uy, + ug +... + wW0- @)s= 145. ®) s = 320. © s = 100. @)s = 150. 1 Cau 3. Cho day s6 (@,) théa man diéu kién 2) = 1,241 —2n = awe)’ n= 1,2,3,.... $6 hang tans bing 4035 4037 4034 4036 5 @) ans = 2018" @ rams = 2018" ©rms = 2018" Ors = 2018" Cau 4. Mot ngudi thiét ké mot cai thap gdm 11 tang. Dién tich bé mat trén cia mdi tang bang ntta dién tich cia mat trén cia tang ngay bén duéi va dién tich cia tang 1 bang nita dién tich cia dé thap (co dién tich 1A 12288 m?). Tinh dién tich cia mat trén cing. @)12 m?’, ®) 10 m’. ©6 mn. ©)8 m. Cau 5. Cho day sé (un) xc dinh béi uy = Lva uny1 = V/u2 +2,Vn € N*. Tong S = ut+u3+...4+u% 991 bang ) 1002002. ®) 1001002. © 1002001. @) 1001001. Cau 6. Trong céc day s6 (wn) sau, hay chon day sé tang. 1 @un =-, Un = —n. © Un =n. Ou = (-1)"n. n uy =2 2 Cau 7. Cho day s6 (un) duge xc dinh nhw sau: , (n > 1). Tinh tong S = Unti + 4Un = 4—5n uz01g — 2u2017- S = 2015-3. 4017, @)s = 2015 43-4017, ©s = 2016 — 3. 42018, @)s = 2016 +3 - 4218, Cau 8. Cho cap sé cong (up) c6 wy = 1 va tong cia 100 s6 hang dau tién 1A 24850. Tinh gia tri cha biéu thie § = ee 1 . uu, -u2U3 usgu4g — UAQU50 9 4 ==. ==. = = 123. @s=a5 ®s=5 ©s-z. Os = 123 wm=5 Cau 9. Cho day sé (u,,) duge xde dinh béi { . Tim s6 hang tong quat ctia day sé. Unt = Un +n n—1)n n—1)n Ou a5 Ou, = 5 nein 5+(n+1)(n+2 ©O©um=5 (n+ In Ou, = ( vi ) Cau 10. Ba sé lap. thanh mot cp sé nhan. Néu sé hang thit hai cong thém 2 ta duge mot cap s6 cong. Sau d6 cong thém 9 véi sé hang thit ba ta lai duge mot cAp s6 nhan. Tinh tong ba sé do. 4 52 Cau 11. Mot da gidc 1di cé 10 canh va cac géc trong cia né lap thanh m6t cap s6 cong véi cong sai d °. Tim géc trong nhé nhat ciia da gidc do. @)26°. ®) 162°. © vor. D 126°. u, = 12 Cau 12. Cho cap sé nhan (un), biét ¢ wz = 043" Tim ug. ug 2 4 4 =—., = . =—. = 78732. @ = 557 6563 ©w= as Duo = 7875 Cau 13. Cho cac khang dinh sau, cé bao nhiéu khang dinh ding? (1) Moi sé hang cia mot cap cong vdi cong sai duong déu 1a s6 dugng. (II) Moi sé hang cia mot cp s6 nhan véi céng boi dudng déu 1A sé duong. (IH) Day sé dude xac dinh béi a, = 1 te la mot day bi chan. (IV) Day sé duge xéc dinh béi a, = 1— . 1A mot day sé giam va khong bi chan dudi. @1. B)4. ©s. @O2. uy =cosa(0<a<z) Un) xdc dinh bdi T+u . Tim ugoiz- Un+1 = 7” 21 . a a @ wor =sin (sox) ®B) uz017 = cos (sear) . a a © wor =sin (5a0m5): D)u2017 = cos (500): Cau 15. Cho hai cap sé cong (un) va (vp) c6 téng cia n s6 hang dau tién lan lugt 1a Sp, Tr. Biét Cau 14. Cho day S, 4nt+1 io, ur T, = on +3 vi moi n € N* a Or os - @> 3 © ws 200 . a . Bn(n+3) + z . * Cau 16. Cho day sé (z,) théa man 7 +22+-++++%, = a vdi moi n € N*. Khang dinh nao duéi_ day lA dang va day di nhat? (xp) la cép s6 nhan véi cong boi dudng. (xp) 1a cap s © (xp) 1a cép s6 nhan véi cong bédi am. ) (en) 1A cap s6 cong véi cong sai am. 1 Uy + Ug Cau 17. Cho mot cap s6 cong (un) c6 u1 = 1, tong 100 sé hang dau bang 24850. Tinh S = 1 1 uz U3 Uag + U50" 49 4 9 @)s = 123. ®Bs=s5 ©s=5 Os-5. 2 w=1 2 2 Cau 18. Cho day sé (un) xdc dinh bdi , . Tinh sé hang thit 2018 cia day sé trén. Unt = 2u, +5 @ wos = 6x 22018 45, B) us = 6 x 27018 _ 5, © wig = 6 x 207 $1. (D) wis = 6 x 277 — 5. 6 cong (uy), thoa man Sg = 92, Sig = 376. Tinh Syq. ®) 946. © 468. ()s52. Sin mm? wis Cau 20. Cho cap s6 cong (un) théa man —* = —z. Tinh —. Sn on uz 35 1225 9 18 33° ® 1089" © 7 7 Cau 21. Cho day s6 (up) xc dinh béi w1 = 1, u2 = 2,tn¢1 = 2un —Un—1+1,Vn > 2. Tinh ugois. @) 2018. (®) 2035154. © 4608289. @)2017. Cau 22. Cho cap sé cong c6 cong sai d = —2 va tong ciia 8 sé hang dau tién Sg = 72. S6 hang dau tién cia cap s6 cong 1A 1 Ou=F Ow =-— @u =-16. Cau 23. Tong cita mot cap sé nhan di v6 han bing ? tong ba s6 hang dau tién ciia cép s6 nhan dé x T a. ‘ > ‘ x bang a7 Tong cia sé hang dau va cong béi cia cap s6 nhan dé bang @o. ©:. O}. Cau 48. Cho cap sé cong (up) c6 s6 hang dau wu; = 3 va cong sai d = 2. S6 hang thit 21 bang @at. ()45. ©.s. @)22. Cau 49. Xac dinh (x,y) dé cac s6 x + Gy; 5a + 2y;8x + y theo tht ty lap thanh cap sé cong va cdc 5 so x — suey — 1; 2x — 3y theo thit ty lap thanh cap sé nhan. Beewde {-1- (F:5)}. ® ew) € {(-%-1; (-13)}. Olay) {eink (x 5) }. D)(e:y) € {(-3\-2 (3)}. 13423433 +...4n3 b b aye Cau 50. Biét jim = 2 (a,b N, a £0), ding thai — 1 phan sé t6i gidn. Gia n? a a 5. ©. )33. 2b de =~ 2, Trong d6 a,b,c la céc s6 nguyén duong, phan aoc Cau 51. Biét I -/* 0 o s6 — téi gian. Tinh T= a? +0? +¢?. c @r=1.. ®r =50. ©r=69. @Or =59. 1 1 Cau 52. Xét tinh tang, giam va bi chan cia day s6 (un), biét un = 1 +5 a 14 Rp tert. n @)Day s6 tang, bi chan. (®) Day giam, bi an trén. © Ba phuong 4n déu sai. (D) Day so tang, bi chan dudi. Cau 53. Véi gid tri nao cia tham sé m thi phuong trinh x? — ma? — 6a — 8 = 0 c6 ba nghiém thuc lap thanh mot cAp sé nhan? ©ms3. Om =~4. Cau 54. Xét tinh tang giam cia day sé u, =n — m=1. @Ba phuong an déu sai. () Day 6 tang. © Day sé khong tang khong giam. (D) Day sé giam. Cau 55. Cho mot ttt gidc li, biét ring 4 gc cita tit gidc d6 lap thanh mét cAp sd cong va goc nhd nhat bang 5 = goc lén nhat. Tim sé do géc nhé nhat cia ttt giae da cho. () 20°. ®) 30°. ©se. ()40°. . Us + 3ug — ug = —21 2 2 soe > Ong (un) thoa man . Tinh tong 15 so hang dau tién cha Cau 56. Cho cap sé 3u7 — 2ug = —34 cap s6 cong (un). @ -274. ~285. © ~253. (@)—244. Cau 57. Cho mot tit gidc li, biét rang 4 gc cita tit gidc d6 lap thanh mét cAp sd cong va géc nhd 1 nhat bang = = goc lén nhat. Tim sé do géc nhé nhat cia ttt giae da cho. Ou. ®) 30°. ©so. 20°. uy = —-2 Cau 58. Cho day sé (un) vdi 9 1 . Cong thitc s6 hang tong quat cia day sé nay 1A Unt = —2 - — Un Om =- n+l ®u =". ©m=- noi Ou =. n Cau 59. Gia tri cia tong 4+ 44+ 444 +--+ + 44...4 (tong c6 2018 sé hang) bing 40 9018 4 na —10 ) @ 5 (10 1) +2018. 5 (3 8). 2019 ©; (“= _ 2018). OF (1028 — 1), . ul =2 : Cau 60. Cho day s6 (u,) xac dinh béi ‘ vdi n > 1. Khang dinh nao sau day la Un+1 = 2un —1 ding? n—-n+4 @un nn an Cau 61. Cho ham sé y = f(x) c6 dé thi y = f’(x) nhu hinh vé. Xét ham s6 g(x) = f(x) — 3 - oo? + 3 + 2017. Cho céc ménh dé dudi day: (D) g(0) < g(1). (11) 2dpin, 9) =g(-1). (IIL) Ham sé g(x)nghich bién trén (—3;—1). (IV) max, 9(2) = max{g(—3),9(1)}- Sé ménh dé dting la un = 3"t1 1. © Un=ntl. Own =14a2r1, @3. ®1. ©. Cau 62. Trong cac day s6 (u,) sau day, day s6 nao lA day s6 giam? __ u=2 @un =|5—nl. { =-1 1 Own =n+-. n Unt = —3Un Unt = ZUn Cau 63. Cho tam giac ABC can tai dinh A. Biét do dai canh day BC, duéng cao AH va canh bén AB theo thi tu lap thanh cp s6 nhan véi cong boi q. Gia tri cia q? bang @vet @ro. Opaaes 2. 2 Cau 64. Ménh dé nao sau day ding? Hai duéng thang cing vudng g6c véi mot mat phang thi song song vdi nhau. Hai dutng thang phan biét cing vudng géc vdi mot dudng thang thi song song véi nhau. ©nuai mat phang phan () Hai mat phang phan biét cimg vudng géc vi mot dudng thang thi song song véi nhau. ing vudng géc véi mot mat phang thi vudng géc véi nhau. wm=1 Cau 65. Cho day . Tim sé nguyén ditong n nhé nhat (un) xc dinh béi 3 . Un+1 = Un +n’, Vn EN sao cho V/un — 1 > 2039190. @)n = 2018. n= 2017. ©n = 2020. @)n = 2019. Cau 66. Ngudi ta thiét ké mot céi thap gdm 10 tang. Dién tich bé mat trén cia méi tang bang ntta x > > x 2 dién tich mat trén cia tang ngay bén dudi va dién tich bé mat cha tang 1 bang 3 dién tich dé thap. Biét dién tich mat dé thap la 6144m?. Tinh dién tich mat trén cing. @) sm’. ®) 4m?. © 12m’. @O) 6m. Cau 67. Xét céc sé thuc dugng a,b sao cho —25, 2a, 3b la cép s6 cong va 2, a+ 2, b—3 1a cap s6 nhan. Khi d6 a? + b? — 3ab bang @)s0. ®)59. ©vw. @®s1. Cau 68. Cho ba sé a,b,c theo thit tu tao thanh cap s6 nhan vdi cong béi khac 1. Biét cfing theo thit tu do chting lan lot 1a sé hang thit nhat, thi tu va thit tam cia mot cap sé cong cong sai lA s 4 0. Tinh ©, s 4 4 @>. 3. ©;. Oo». Cau 69. Véin >0 Day sé Fibonacci dugc Leonardo Fibonacci, mot nha toan hoc ngudi Y, cong bé vao nam 1202 trong cuén séch “Liber Abacci”- Sach vé ton dé qua hai bai toan: “ Bai todn con tl va bai toan “ t6 ctia mot ong duc”. Day sé nay hau nhuw bién hda vo tan. Chinh diéu dé lam cho nhiéu nha Ton hoc (chuyén nghiép lan nghiép du) va ca nhing ngudi binh thudng nghién cttu, khaém pha Newdi ta chitng minh duge ring cong thite tong quat cho day Fibonacci la: 1+v5\" (1-v5\" 2 - 2 S6 Lucas la mot day s6 duge dat tén nhim vinh danh nha Todn hoc Francois Edouard Anatole Lucas, ngudi da nghién cttu day sé Fibonacci, day sé Lucas va céc day tuong ty. Day s6 gom thudng 145 2 _ v5 Fin) = gitfa hai sé Lucas lién nhau sé hoi tu dén gidi han bang ti 1é vang { y = . Cong thtte tong H=( 9 (68 $6 Lucas lién hé vdi s6 Fibonacci béi hang dang thiic sau: quat cia sé Lucas: Ln = Fn-2+ Fn Hay tim tong Sin) = Fr—2 + Fra + Fn + Frys, biét Ln = 18. @s. ®)29. ©47. O13. Cau 70. Cho biét a,b,c 1a ba canh cia mot tam gidc va theo thit ty lap thanh mot cap so cong va c4p sé nhan. Khang dinh nao sau day sai? @ac =e. () (1 —a)(e— 1) = (6-12. 1 1 2 ©-=4+-=5. (@) (a+ (e+ 1) = (b+ 12. c a b 2 =2 2 Cau 71. Cho day s6 (u,) xée dinh béi 4“ véi n > 1. Khang dinh nao sau day 1A Un+1 = 2Un — 1 ding? 2 @un = uot Un =n+l1. © un = 3"tt 1, Oun =142"1, Cau 72. Cho day s6 (un) dude xac dinh béi v1 = 0 va uny1 = n+uUn Vn > 1. Tinh gid tri cia uais. A) 23436. ®) 2381. © 23653. () 46872. Cau 73. Cho hinh chép S.ABCD cé déy ABCD la hinh chit nhat, SA 1 (ABCD), SA = AB =a, BC = 2a. Cosin ciia géc giita SC va DB bang 2 1 1 -1 @2 Oa ©% os Cau 74. Tim x biét 1, 2?, 6 — 2 theo tht ty lap thanh cp s6 nhan. @e=+v2. ®-«=+v3. ©r=#1. @)x = +2. Cau 75. Tim tat ca cdc s6 ty nhién k sao cho Ch, ChE chy? theo thit ty lap thanh mot cap sé cong. Q@k=4,k=5. Bk=7,k=8. ©O©k=3,k=9. Ok =4,k=8. Cau 76. Cho day sé (u,) xdc dinh béi: uy = —2, up = 3up—1 — 1, Vn > 2. Xac dinh sé hang tong quat ctia day sé da cho. 5 5 1 5 al @an=-3 0343. B) ty = -5 3" 4+ 5. Om=5°3 3” +3 Dw = “3742. mio 2 Cau 98. Goi S$ la tap hgp cdc nghiém thudc khoang (0; 1007) cia phuong trinh (sin + cos 5) + V3cosx = 3. Tinh tong cdc phan ttt cia S. 75250 74007 755070 73750 @ © © 300 3 3 Cau 99. Xét nam ménh dé sau, véi (un) 1a mot cAp sé cong vo sé phan tit, ui 1a mot sd hang c6 gid tri xdc dinh. Biét day (u,) cé mot s6 hang bang 0, uy 4 0. 1) Moi s6 hang cia (un) déu bang 0. 2) Moi sé hang khac cia (wn) déu 1a sé dugng. oy 2 m. am. oy ( ( (3) Moi sé hang khac ciia (un) déu 1a si (4) Chi cé mét sé hitu han sé hang 1a s (5) Chi cé mét sé hitu han sé hang 1a s6 duong. Trong nam ménh dé trén, s6 ménh dé sai 1A @3. ®1. ©2z @)4. Cau 100. Tong cac nhan dinh sau, c6 bao nhiéu nhan dinh sai? 1 (1) 142434-04n—2@#) Wren). 2 ‘ (2) Un = v la mot day sé tang. (3) un = —sinn la mét day sé tang. on on ©. O» ‘ oe =1 4 A Cau 101. Cho day s6 (u,) xac dinh béi m1 . Tinh so hang tht 2018 cia day. Unti = 2u, +5 @ woos = 3.225 + 5. ugois = 3.207 +1, © apis = 3.228 —5. (DB) usps = 3.27 — 5. Cau 102. Cho mot day sé cé cac s6 hang dau tién 1A 1, 8, 22, 43. cia day s6 d6 lap thanh mot cap sé cong: 7, 14, 21, ..., 7. Hoi ctia day s6 da cho. @) 100. ®) 102. © 103. @®)101. Cau 103. Tim ba sé hang lién tiép cia mot cAp sé cong biét tong cia ching bing —9 va tong cdc binh phuong ctia ching bang 29. @) -4;-3; 2. ®) -3;-2;-1. ©1;2:3. @)-2; -1:0. . Hiéu cita hai sé hang lién tiép 5351 1a sd hang thit bao nhiéu = xe eh van Ht oe 1 n-1 a Cau 104. Cho day s6 xdc dinh bdi wy = 1, upyi = 3 (2 + a) n € N*. Khi d6 uaoig bang 92017 1 22018 1 92017 1 92016 1 @ 32010 + 50 19° 3a017 + 019° © 30018 + 5019" © 30017 + 5019" Cau 105. Cho cap sé cong (un), biét uy = 1, S, = 55, d =1. Khi do gia tri cia n 1A bao nhiéu? @n=9. ®n=10. ©n=u. @M)ne {10;—11}. Cau 106. Cho cap sé cong (uy) c6 uy = —2 va cong sai d = 3. Sé hang uy la @w =4. Bw =-6. Ow =--5. Ow =1. Cau 107. C6 bao nhiéu cap sé nhan c6 5 sé hang? Biét ring téng 5 sé hang do la 31 va tich cia ching la 1024? @1. ®2 ©. Ds. 10 Cau 108. Cho hinh vudng AiBiC;D,; c6 canh bang 1. Goi Agyi, BryisCr+1, Dey thit ty la trung diém céc canh A,By; Di BeCpiCeDeiDpAp (vei k = 1,2,...). Chu vi cia hinh vudng Cy ApoisBa1sC2018D2018 1a v2 v2 v2 v2 @ 21007 * 22017 * © 22018" © 21006" At By Cau 109. Cho day s6 (a) xdc dinh béi a1 = V2, an41 = V2+ an, n € N*. Ménh dé nao duéi day la ménh dé ding? @ (xp) la cép s6 nhan. ®) lim In = 2. ©lmz,, = +00. ) (en) la day s6 giam. Cau 110. Day sé (up) xdc dinh béi u, = 3n — 2, véin > 1. Tinh tong S =u, + ug +...+ uo. @s = 15. ®)s = 320. ©s = 1060. @)s = 150. Cau 111. Cho cdc s6 5a — y, 2a + 3y, x + 2y theo thit ty lap thanh cp s6 cong; cdc s6 (y + 1)"; xy +1, (a —1)? theo thi ty lap thanh cap s6 nhan. Tim (a;y). @tew = 0), (1:4), (--F). ® tow = 0:0), (24), (2-3). Own = 00), (23). (2B). Ole = 010), (4:4), (2-3). said = —3 va u3 + u3 + uj dat gid tri nhé nhat. Tinh tong Sio9 cia 100 sé hang dau tién cia cAp s6 cong do. @) Stoo = - 14400. Stoo = 14250. © Sto = —15450. (DB) Sio0 = 14650. Cau 113. Tinh tong S=1+11+---+ 111. nsé1 10 @y tort =) - 5. ® | (u0"-y-<. I n 10 n — (10"-! — 1) —-. — (10"-!-1)+—. ©x( )-% Ox | )+5 Cau 114. Cho day sé (un) duge xdc dinh béi uy = @ Va Un41 = 4un(1—un) véi moi n = 1,2,-++ . C6 bao nhiéu gid tri cia a dé uz01g = 0? QP a1, 3 © 41. Or 41. Cau 115. Day sé (un) théa man S$, = uy +u2+...+ un = n?. Tinh up. @ uy = 121. uy = 20. © uy» = 14. O) ws = 23. Cau 116. Ba sé lap thanh mot cap sé nhan. Néu sé hang thit hai cong thém 2 ta duge mot cap s6 cong. Sau d6 cong thém 9 véi > hang thit ba ta lai dude m6t c4p sé nhan. Tinh tong ba sé do. 5 25 B35 “35° 3 Cau 117. Cho mot day sé cé cac s6 hang dau tién 1A 1, 8, 22, 43. cia day s6 d6 lap thanh mot cap sé cong: 7, 14, 21, ..., 7. Hoi ctia day s6 da cho. @)101. ®) 100. © 103. @) 102. u=2 Cau 118. Cho day sé (un) théa man un +V2—1 ,Vn €N*. Tinh uzois Un+1. = 1—(V2-1)tn @ wors =7-5v2. B®) wos =74+5y2. © wp is=2. D) wos =7T+Vv2. |r oF . Hiéu cita hai sé hang lién tiép 5351 1a sd hang thit bao nhiéu 1 Cau 119. Trong cdc day sé sau, day s6 nao la day sé tang? @un = nt 3 Un = © Un = - Dun =n? +2n. n+1 Cau 120. Cho tam gidc ABC c6 do dai cac canh 1a a, b, c theo thit ty lap thanh mot cap s6 cong. A c a Biét tan 2 tan S -2 (z,y € N, phan s6 téi gidn), tinh gid tri x + y. y @ on ©» Os. Cau 121. Cho tong Sy = 1? 42? +...n?. Khi d6, cdng thitc cha S; la @s. Os- 6, ©s.- _ n(2n + (en + Dy Os, = _ n(n — Hin + 1) Cau 122. Trong cac day sé (un) sau day, day sé nao bi chan? 1 —1)" @) un = 3.2". Bm =n+=. Om = Vn? +1. Dun = =a —— n mn Cau 123. Cho cap s6 cong (uy) c6 cong sai d. Tim diéu kién cia d dé (u,) 1a day s6 tang. @ ld >1. ®d>1. ©d<o. @DMa>o. Cau 124. Cho cap sé nhan c6 7 sé hang, sé hang tht tu bang 6 va sé hang thtt bay gap 243 lan sé hang thit hai. Tim cac s6 hang con lai cita cép s6 nhan do. 2 2 @u = gi = gus = 2:u5 = 21; ug = 54; u7 = 162. 2 2 Bu = 9 = 53 U3 = 2;u5 = 18: ue = 54; u7 = 162. Ou = ge = gous = 2;u5 = 18; ug = 54; u7 = 162. 2 2 Du = piu = Bis = 2;u5 = 18; ug = 54; uz = 162. Cau 125. Cho day sé (un) duge xée dinh béi uy = 2,un = 2un-1 + 3n —1Vn > 2. Biét rang cong thie tong quat ciia day s6 da cho c6 dang up = a-2"+bn+cVn > 2, trong dé a,b,c 1a céc s6 nguyén. Khi do, ting a+b +c cé gia tri bing @-3. ® -4. ©s. Or Cau 126. Ban Nam [a sinh vién ciia mét trudng Dai hoc, muén vay tién ngan hang voi lai suat wo dai trang trai hoc phi hoc tap hang nam. Dau méi nam hoc, ban ay vay ngan hang véi sé tién 10 triéu déng véi lai suat 4% mét nam. Tinh sé tién ma Nam ng ngan hang sau 4 nam hoc, biét rang trong 4 nam d6, ngan hang khong thay déi lai suat (két qua lam tron dén nghin ding). @) 41600000 dang. 44163000 déng. (©) 42465000 ding. (DB) 46794000 dang. . us + 3u3 — ug = —21 Cau 127. Cho cAp sé cong (up) théa man { .” 8 2 . Tinh S = ug tus +--+ +ugo. 3u7 — 2ug = —34 (A) -1222. ®) -1242. © -1276. ®) -1286. Cau 128. Cho day hinh vung Hj, Ho,..., Hp,... V6i méi s6 nguyén duong n, goi Un, Pr, Sn lan hiot la do dai canh, chu vi va dién tich cia hinh vuéng Hy. Trong caéc khang dinh sau, khang dinh nao sai? @Néu (un) 1a cép s6 cong véi cng sai khéc 0 thi (P,) cing 1a cap sé cong. ( ( ©néu (un) 1a cép s6 nhan véi cong boi dudng thi (P,) cing 1a cAp sé nhan. (®)Néu (un) 1a cép s6 cong véi cong sai khéc 0 thi (S;,) cing 1A cép s6 cong. (D)Néu (un) 1a cép s6 cong véi cong sai khac 0 thi (5,,) cing 1A cép s6 cong. Cau 129. Cho mot cap s6 cong (up) c6 uy = 1 va biét téng 100 sé hang dau bang 24850. Tinh 1 1 uyug u2u3 uUagui 49 9 4 @)s = 123. Bs= x5 ©S= 55 Os=5. 12 ©néu ton tai mot sé m sao cho up, (D)Néu ton tai mot s6 M sao cho up, m, Wn € N* thi (up) 1a day sé bi chan. 2 < M,Wn € N* thi (u,) 1a day sé bi chan. Cau 153. Téng cia n sé hang dau tién cia mot day s6 (an),n > 11a Sp = 2n? + 3n. Khi d6 (an) 1a mét cp s6 cong véi cong sai bang 1. (an) 1a mét cap s6 nhan véi cong boi bang 1. (an) 1a mét cp s6 cong véi cong sai bang 4. (ay) 1a mét cap s6 nhan véi cong boi bang 4. GOG@®D Cau 154. Tim tat cA cac gid tri cia tham s6 m dé phuong trinh 2° — 32? + mz + 2m—1=0c6 3 nghiém phan biét lap thanh mot cap s6 cong. @m=1,m=2. ®m=-1. ©m=2. ()m =1. Cau 155. Cho day sé (up) 6 s6 hang téng quat up, = sin véin € N*. Dat S, = uy +ugt:-++Up- Tim khang dinh ding trong céc khang dinh sau. @) Sooi7 <0. Soo20 = 0. © Sooig > 0. ©) S218 =0. Cau 156. Cho cap s6 cong (un) théa man w49 — wig = 9, uty — UZg = 153. Tim wa9. 17 29 @) ua» = 29. Ug9 = z © Ugg = z Dw =17. Cau 157. Bén sé tao thanh mot cap s6 cong c6 tong bang 32 va tong cdc binh phugng cia ching bang 336. Tich ciia bon sé do 1a (A) 5760. ®) 15120. © 1920. @) 1680. Cau 158. Tim tat ca cac gid tri cha x dé ba sé 1—2, 2”, 1+2 theo tht ty lap thanh cap sé cong. @er=-1. @®er=.. ©r=+2. @)x = +1. Cau 159. Phuong trinh x? + az +b = 0 c6 ba nghiém phan biét lap thanh cap s6 cong. Chon khang dinh ding. @b=0,a<0. @b=ta=-2. ©Ob=0,a=1. @M)b=-2, a=1. Cau 160. Mot nguéi giti tiét kiém ngan hang theo hinh thitc giti gop hang thang. Lai suat tiét kiém giti gop cé dinh 0,55%/thang. Lan dau tién ngudi do giti 2.000.000 dong. Cit sau mdi thang ngudi do giti nhiéu hon sé tién da gtti thang trudc do 1a 200.000 dong. Hoi sau 5 nam (ké ti lan giti dau tién) ngwi dé nhan duge tong sé tién cA vén lan lai 1a bao nhiéu? (A) 618051620 ding. 539447312 dong. (©) 597618514 ding. — (D) 484692514 ding. w=1 2 4 Cau 161. Cho day (un) dude xdec dinh bdi : y- 6 hang tong quat cia day sé 1a Until = Un +1 n— 1)n(2n + 2 n(2n + 1)(n+1 Ban 14 Wan 2) Bou = 14 MAEDOLD, 2 x —1)n(2n-1 © tat ca cdc khang dinh A, B, C déu sai. Dun =14+ (ea tnGn 1) Cau 162. Cho day s6 (an) théa man x1 + 22 +°++++an = ines) véi moi n € N*. Khang dinh nao _duéi day 1a ding va day da nhat? (an) la cép 86 cong vdi cong sai am. (an) la cép sé cong véi cong sai duong. © (an) la cép s6 nhan véi cong bédi am. ) (an) 1a cép sé nhan véi cong boi dugng. Cau 163. X4c dinh sé hang uois cia day (un) dude xac dinh béi u=2 svn > 2. Un = 2Un—-1 + 3n—1 ) woos = 5 - 207 — 6059. B) wos = 5 - 270'8. © wig = 22. (D) ups = 5 - 22018 — 6059. Cau 164. Giai phuong trinh 1+ 8+ 15+422+---+a = 7944. @ x =351. ®)x = 220. © x =407. @)« = 330. Cau 165. Cho tit giée déu ABCD cé canh bing a. Khoang cach tiv A dén mat phang (BCD) bing av3 av6 av3 av6 @s. ee O=; > Cau 166. Cho cp sé nhan (up) c6 hang dau wu; = 2 va tong cia 8 s6 hang dau tién Sg = 6560. Tim cong bdi q cia cép s6 nhan da cho. @q=-3. ®i-}. ©q=3. @M q=33. Cau 167. Cho hinh vuéng ABCD c6 cac canh bang a, va cé dién tich $}. N6i bén trung diém A), Bi,Ci,D) theo tht tw cia bén canh A dD, D AB,BC,CD,DA ta duge hinh vuong thit hai c6 dién tich $2. Tiép D. tuc lam qué trinh trén ta dugc hinh vuong thit ba la Ap BoC2D, cd 2 2 dién tich $3,... va ctt tiép tuc lam nhu thé ta dude céc hinh vuong lan ligt c6 dién tich $4,55,..., S100 (tham khao hinh vé bén). Tmh tong 41 C1 S=S1+S$2+-+++ Stoo. AD 2 D 2(9200 4 (2200 4 (29 1 @s= 2100 oe. @s-20 ©s=20 Os= 500" Cau 168. Tinh S = 1+42-243-2? +--+. +2018. 27017, G28 41, 2017-27984, ©2017-2741. D)2017- 2718 — 1 HET 16 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 BDF DD DF F&F DOD F&F F&F BD BP Fe SD 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 DAP AN Cc 86 B 87 A 88 C 89 D 90 C 91 C 92D 93 A 94D 95 C 96 97 98 Go OD BP YD 99 100 D 101 C 102 D 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 Go BD OD eS a Oo BF BDFD FD Pp BP BP F&F BD Se 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 5 oD +} B BD DP DBD wD eS Cc 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168