第1课时等差数列的概念及通项公式1.在△ABC中,三内角A,B,C成等差数列,则角B等于()A.30°B.60°C.90°D.120°解析:∵A,B,C成等差数列,∴2B=A+C.又A+B+C=180°,∴B=60°.答案:B2.等差数列{an}中,首项a1=6,公差d=7,如果an=2015,则n等于()A.278B.280C.288D.298解析:∵a1=6,d=7,∴an=6+7(n-1)=7n-1.∴由an=2015得,7n-1=2015,n=288.答案:C3.已知数列{an}为等差数列,且a1=2,a2+a3=13,则a4+a5+a6等于()A.40B.42C.43D.45解析:设公差为d,则a1+d+a1+2d=2a1+3d=4+3d=13,解得d=3,所以a4+a5+a6=(a1+3d)+(a1+4d)+(a1+5d)=3a1+12d=42.答案:B4.设x是a与b的等差中项,x2是a2与-b2的等差中项,则a,b的关系是()A.a=-bB.a=3bC.a=-b或a=3bD.a=b=0解析:由等差中项的定义知:x=,x2=,∴,即a2-2ab-3b2=0.故a=-b或a=3b.答案:C5.首项为-24的等差数列,从第10项起开始为正数,则公差d的取值范围为()A.d>B.d<3C.≤d<3D.
