Question

設(shè)等差數(shù)列{a_n}的公差不為0，其前n項(xiàng)和是S_n．若S₂=S₃，S_k=0，則k=______．

Answer 1

∵S₂=S₃，∴S₃-S₂=0=a₃，∴a₁+2d=0，∴a₁=-2d≠0．
又S_k=0，則ka1+

k(k-1)

2

d=0，∴2a₁+（k-1）d=0．
把a(bǔ)₁=-2d≠0．代入上式得-4d+（k-1）d=0，化為-4+k-1=0，解得k=5．
故答案為5．