Question

已知{an}是一个公差大于0的等差数列且满足a3a6=55,a2+a7=16求数列{an}的通项公式

Answer 1

∵an是等差数列

∴a2+a7=a3+a6

{a3+a6=16

{a3*a6=55

解得：a3=5,a6=11;a3=11,a6=5

d=(11-5)/(6-3)=2,或d=(5-11)/(6-3)=-2

a1=a3-2d=1,或a1=a3-2d=15

an=a1+(n-1)d=2n-1,或an=a1+(n-1)d=17-2n