等差数列{an}的前n项和为Sn=n2+2n+a+2,则常数a=( )
A.-2
B.2
C.0
D.不确定
∵等差数列{an}的前n项和为Sn=n2+2n+a+2,
∴a1=S1=1+2+a+2=5+a,
a2=S2-S1=(4+4+a+2)-(5+a)=5,
a3=S3-S2=(9+6+a+2)-(4+4+a+2)=7,
∵{an}是等差数列,
∴2a2=a1+a3,
∴2×5=5+a+7,
解得a=-2.
故选A.
等差数列{an}的前n项和为Sn=n2+2n+a+2,则常数a=( )
A.-2
B.2
C.0
D.不确定
∵等差数列{an}的前n项和为Sn=n2+2n+a+2,
∴a1=S1=1+2+a+2=5+a,
a2=S2-S1=(4+4+a+2)-(5+a)=5,
a3=S3-S2=(9+6+a+2)-(4+4+a+2)=7,
∵{an}是等差数列,
∴2a2=a1+a3,
∴2×5=5+a+7,
解得a=-2.
故选A.