问题
填空题
若数列{an}为等差数列,a15=8,a60=20,则a75=____________.
答案
24
解法一:∵a15=a1+14d,a60=a1+59d,
∴
解得a1=
,d=
.
∴a75=a1+74d=24.
解法二:∵{an}为等差数列,
∴a15,a30,a45,a60,a75也成等差数列.
设其公差为d′,则a15为首项,a60为第4项.
∴a60=a15+3d′,即20=8+3d′,解得d′=4.
∴a75=a60+d′=24.
解法三:∵a60=a15+(60-15)d,
∴d=
.
∴a75=a60+(75-60)d=24.
