问题
选择题
等差数列{an}满足a42+a72+2a4a7=9,则其前10项之和为( )
A.-9
B.-15
C.15
D.±15
答案
∵等差数列{an}满足a42+a72+2a4a7=9,则有 (a4+a7)2=9,∴a4+a7=±3.
故其前10项之和为S10=
=10(a1+a10) 2
=±15,10(a4+a7) 2
故选D.
等差数列{an}满足a42+a72+2a4a7=9,则其前10项之和为( )
A.-9
B.-15
C.15
D.±15
∵等差数列{an}满足a42+a72+2a4a7=9,则有 (a4+a7)2=9,∴a4+a7=±3.
故其前10项之和为S10=
=10(a1+a10) 2
=±15,10(a4+a7) 2
故选D.