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河南省2023-2024学年新乡市高二期末(上)测试(24-306B)数学.考卷答案试卷答案
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Overtheyears,Arecibohasfaceddangeranddamage,butithasalwaysendured.Initslifetime,ithasexperiencedearthquakesandstorms,includingthehurricanethatspoiltPuertoRicoin2017,whichdamagedsomeofthedish.ThetroublebeganinAugust.Ametalsupportcableweighingthousandsofpoundsslippedoutofitssocket(anddroppedsharplyintothecavernous,1,000-foot-wideradiodishinthemiddleofthenight.Thecable,installedinthe1990s,wasconsideredfairlynewforanobservatorythatbeganoperationsin1963,andtheincidentconfusedArecibo'sofficials.Thecable"definitelyshouldnothavefailedinthewayitdid,"AshleyZauderer,theAreciboprogramdirectorattheNationalScienceFoundation,whichownsthetelescope,said.Butearlierthismonth,justdaysbeforeengineerswerescheduledtotrytostabilizethetelescope,anotherpieceofhardwarecamesmashingintothedish.Amaincable,oneoftheoriginalsinstalledwhentheobservatorywasbuilt,hadcracked,causingevenmoredamage.Engineersarenowworkingtoquicklyoutlinedaplantopulldownthetelescopebeforeitcollapsesonitsown.Arecibo'sfailureisadifferentfatethanastronomersareusedto.Hardwareofallsortsagesandbreaks-Hubble,anotherfamedtelescope,isoperatingwithfewerworkingpartsthanitlaunchedwith30yearsago.Butitisunusualtowreckanobservatorybecauseyouhavenootherchoice,andsounexpectedlytoo.32.WhatwillhappentoArecibo?A.Itwillbedestroyed.B.Itwillberebuilt.C.Itwillberepaired.D.Itwillbestabilized.33.Whatdoestheunderlinedword"endured"meaninparagraph2?A.Avoided.B.Survived.C.Endangered.D.Forgotten.34.WhichcanbestexplainAshleyZauderer'smessageinparagraph3?A.Arecibocanberemovedeasily.
分析求出an，求出a1，a2，a3，再由a22=a1•a3能够得到常数a的值．
解答解：因为数列{an}的前n项和Sn=2n+1-c所以S1=4-c，S2=8-c，S3=16-c，
又因为a1=s1，a2=s2-s1，a3=s3-s2，所以a1=4-c，a2=4，a3=8，
根据数列{an}是等比数列，可知a1a3=a22，所以（4-c）×8=16，解得，c=2．
故选：A．
点评本题考查了数列中Sn与通项an的关系应用，等比数列的定义，考查转化、计算能力．
