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:B
2.等差数列{an}中,首项a1=6,公差d=7,如果an=2015,则n等于( )
A.278 B.280 C.288 D.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:C
3.已知数列{an}为等差数列,且a1=2,a2+a3=13,则a4+a5+a6等于( )
A.40 B.42 C.43 D.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:B
4.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=-b B.a=3b
C.a=-b或a=3b D.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.
