Question

等差数列An 满足A2=3 ,Sn-Sn-3=51 求Sn=100 n= 详解

Answer 1

Sn-Sn-3=51

即An+An-1+An-2=51

假设等差值为x

[An-1+x ]+ An-1+ [An-1-x]=51

即An-1=17

Sn=(A1+An)n/2=(A2-x +An-1+x) n/2=(3+17)n/2=10n

因为Sn=100

所以n=10