已知数列{an}为等差数列,若a4+a7+a10=17,a4+a5+a6+…a12+a13+a14=77,且ak=13,则k=

问题描述:

已知数列{an}为等差数列,若a4+a7+a10=17,a4+a5+a6+…a12+a13+a14=77,且ak=13,则k=

a4+a7+a10==3a7=17
a7=17/3
a4+a5+a6+……+a14=11a9=77
a9=7
2d=a9-a7=4/3
d=2/3
a1=a7-6d=5/3
ak=a1+(k-1)d=5/3+(k-1)*2/3=13
k=18