北京市部编版高中英语必修第一册第6章数列练习题

2026年北京市部编版高中英语必修第一册第6章数列练习题一、单项选择题（总共10题，每题2分，共20分）1.Inthesequence{a_n},ifa_1=3anda_n+1=a_n+2(n∈N),thenthegeneralformulafora_nis______.A.n^2+2n+1B.2n^2+n+1C.2n+1D.n^2+2n+32.Whichofthefollowingsequencesisanarithmeticprogression?A.a_n=2^nB.a_n=n(n+1)C.a_n=3n-5D.a_n=(-1)^n3.Inageometricprogression,ifa_3=8anda_5=32,thenthecommonratioqis______.A.2B.-2C.4D.-44.Thesumofthefirst10termsofthearithmeticprogression5,8,11,...is______.A.275B.280C.285D.2905.Thesumoftheinfinitegeometricseries1+1/2+1/4+...is______.A.1B.2C.1/2D.46.Ifa_nisanarithmeticprogressionanda_4=10,a_7=19,thena_10is______.A.28B.29C.30D.317.Theproductofthefirst5termsofageometricprogressionis32,andthefirsttermis2.Thecommonratioqis______.A.2B.1/2C.4D.1/48.Thesumofthefirstntermsofthearithmeticprogression-3,-1,1,...isequalto66.Thevalueofnis______.A.12B.13C.14D.159.Inageometricprogression,ifa_2=6anda_4=54,thena_6is______.A.486B.162C.324D.24310.Thesumofthefirst20termsofthearithmeticprogression7,10,13,...is______.A.860B.880C.900D.920二、填空题（总共10题，每题2分，共20分）1.Thegeneralformulaforthenthtermofthearithmeticprogression5,9,13,...is______.2.Ifa_nisageometricprogressionanda_3=12,a_5=48,thena_7=______.3.Thesumofthefirst8termsofthegeometricprogression3,6,12,...is______.4.Thecommondifferenceofthearithmeticprogression2,5,8,...is______.5.Thesumoftheinfinitegeometricseries1/4+1/8+1/16+...is______.6.Ifa_nisanarithmeticprogressionanda_5=15,a_10=30,thenthecommondifferencedis______.7.Thegeneralformulaforthenthtermofthegeometricprogression1,2,4,...is______.8.Thesumofthefirst15termsofthearithmeticprogression-2,0,2,...is______.9.Ifa_nisageometricprogressionanda_1=5,a_4=80,thenthecommonratioqis______.10.Theproductofthefirst4termsofthegeometricprogression2,4,8,...is______.三、判断题（总共10题，每题2分，共20分）1.Allarithmeticprogressionsaregeometricprogressions.(True/False)2.Thesumofthefirstntermsofageometricprogressionisalwaysgreaterthantheproductofthefirstnterms.(True/False)3.Ifa_nisanarithmeticprogression,thena_n=a_1+(n-1)d.(True/False)4.Thesumoftheinfinitegeometricseries1+2+4+...convergestoafinitevalue.(True/False)5.Ifa_nisageometricprogressionanda_2=6,a_3=12,thenthecommonratioqis2.(True/False)6.Thesumofthefirst10termsofthearithmeticprogression3,7,11,...is200.(True/False)7.Ifa_nisageometricprogressionanda_1=2,a_5=32,thena_3=8.(True/False)8.Theproductofthefirst5termsofthegeometricprogression1,3,9,...is243.(True/False)9.Thesumofthefirst8termsofthearithmeticprogression5,7,9,...is72.(True/False)10.Ifa_nisageometricprogressionanda_4=16,a_6=64,thena_5=32.(True/False)四、简答题（总共8题，每题2分，共16分）1.Explainthedifferencebetweenanarithmeticprogressionandageometricprogression.2.Derivetheformulaforthesumofthefirstntermsofanarithmeticprogression.3.Whatisthegeneralformulaforthenthtermofageometricprogression?4.Howdoyoufindthesumofaninfinitegeometricseries?5.Describetheprocessofdeterminingthecommondifferenceandcommonratioofasequence.6.Whyisthesumoftheinfinitegeometricseries1+1/2+1/4+...equalto2?7.Howcanyouverifyifagivensequenceisanarithmeticprogressionorageometricprogression?8.Whataretheconditionsforageometricprogressiontohaveafinitesum?五、应用题（总共8题，每题4分，共24分）1.Thefirsttermofanarithmeticprogressionis4,andthecommondifferenceis3.Findthesumofthefirst20terms.2.Thesumofthefirst5termsofageometricprogressionis31,andthefirsttermis2.Findthecommonratio.3.Inageometricprogression,ifa_3=12anda_6=96,findthefirsttermandthecommonratio.4.Thesumofthefirst10termsofanarithmeticprogressionis275,andthelasttermis30.Findthefirstterm.5.Thesumofthefirst8termsofageometricprogressionis255,andthecommonratiois3.Findthefirstterm.6.Inanarithmeticprogression,ifa_4=10anda_9=25,findthesumofthefirst12terms.7.Thesumofthefirst6termsofageometricprogressionis63,andthefirsttermis1.Findthecommonratio.8.Thesumofthefirst15termsofanarithmeticprogressionis450,andthecommondifferenceis2.Findthefirstterm.【标准答案及解析】一、单项选择题1.C解析：a_n+1=a_n+2→a_n+1-a_n=2→a_n=a_1+(n-1)×2=3+2(n-1)=2n+1.2.C解析：a_n=3n-5→a_n+1-a_n=3→arithmeticprogression.3.A解析：a_5=a_3×q^2→32=8q^2→q^2=4→q=2.4.B解析：S_10=n/2×(a_1+a_n)=10/2×(5+28)=5×33=165.5.B解析：S=a/(1-r)=1/(1-1/2)=2.6.C解析：d=(a_7-a_4)/(7-4)=(19-10)/3=3→a_10=a_7+3×3=19+9=28.7.A解析：a_1×a_2×a_3×a_4×a_5=32→2q×2q^2×2q^3×2q^4×2q^5=32→2^10×q^15=32→q=2.8.A解析：S_n=n/2×(2a+(n-1)d)=66→n/2×(-6+(n-1)×2)=66→n^2-7n+66=0→n=12.9.A解析：a_4=a_2×q^2→54=6q^2→q^2=9→q=3→a_6=a_4×q^2=54×9=486.10.B解析：S_20=20/2×(7+47)=10×54=540.二、填空题1.a_n=4n+12.1923.15364.35.16.37.a_n=2^(n-1)8.909.210.64三、判断题1.False解析：arithmeticprogressionhasaconstantdifference,whilegeometricprogressionhasaconstantratio.2.False解析：e.g.,1+2+4=7,1×2×4=8.3.True4.False解析：1+2+4+...diverges.5.True6.True7.True8.True9.True10.True四、简答题1.Arithmeticprogressionhasaconstantdifferencebetweenterms,whilegeometricprogressionhasaconstantratio.2.S_n=n/2×(2a+(n-1)d).3.a_n=a_1×q^(n-1).4.S=a/(1-r)for|r|<1.5.Forarithmeticprogression,findd=a_n-