已知等差数列{an}中,a2=3,a8=7,求a5和S5

题目

已知等差数列{an}中,a2=3,a8=7,求a5和S5

答案

a8=a2+d(8-2)
7=3+6d
d=2/3
a5=a2+3d
=3+2
=5
a2=a1+d
a1=a2-d
=3-2/3
=7/3
an=7/3+2/3(n-1)
=2n/3-5/3
S5=5(7/3+5)/2=55/3