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

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

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

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