数列{an}中,已知an=(-1)n•n+a(a为常数)且a1+a4=3a2,则a=_,a100=_.

问题描述:

数列{an}中,已知an=(-1)n•n+a(a为常数)且a1+a4=3a2,则a=______,a100=______.

由题意可得,a1=a-1,a2=a+2,a4=a+4
∵a1+a4=3a2
∴a-1+a+4=3(a+2)∴a=-3
∴a100=(-1)100×100-3=97
故答案为:-3,97.