Question

若n為等差數(shù)列-4，-2，0，…中的第8項(xiàng)，則二項(xiàng)式(x2+

2

x

)n展開(kāi)式中常數(shù)項(xiàng)是第______項(xiàng)．

Answer 1

等差數(shù)列的通項(xiàng)為a_n=-4+（n-1）×2=2n-6
∴a₈=16-6=10
∴(x2+

2

x

)n=(x2+

2

x

)10展開(kāi)式的通項(xiàng)為
Tr+1=2r

C

r10

x20-

5r

2

令20-

5r

2

=0
解得r=8
∴展開(kāi)式中常數(shù)項(xiàng)是第9項(xiàng)
故答案為9