It is proved that let the first n terms of the sequence {an} sum Sn = an 2+bn (a and b are constants),

When n= 1, a 1=S 1=a+b,

n & gtAt 1 an = sn-s

When n= 1, the above formula also holds.

∴a<； n+ 1 & gt； -an=2a，

∴{an} is arithmetic progression.