2.2.2　等差数列性质及应用

等差数列主要性质(1)an=am+(n-m)d(m,n∈N*).(2)若m+n=p+q(m,n,p,q∈N*),则am+an=ap+aq.尤其地,若m+n=2p,则am+an=2ap.(3){an}公差为d,则d>0{an}为递增数列;d<0{an}为递减数列;d=0{an}为常数列.(4)若{an},{bn}分别是以d1,d2为公差等差数列,则{pan+qbn}是以pd1+qd2为公差等差数列.(5)若{an}是等差数列,公差为d,则ak,ak+m,ak+2m,…(k,m∈N*)组成公差为md等差数列.