若等差数列an的前n项和为Sn,且满足Sn/S2n为常数,则称该数列为S数列若首项为a1的等差数列an(an不为常数)为“S数列”,试求出其通项公式

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若等差数列an的前n项和为Sn,且满足Sn/S2n为常数,则称该数列为S数列若首项为a1的等差数列an(an不为常数)为“S数列”,试求出其通项公式
若等差数列an的前n项和为Sn,且满足Sn/S2n为常数,则称该数列为S数列
若首项为a1的等差数列an(an不为常数)为“S数列”,试求出其通项公式

若等差数列an的前n项和为Sn,且满足Sn/S2n为常数,则称该数列为S数列若首项为a1的等差数列an(an不为常数)为“S数列”,试求出其通项公式
设Sn/S2n=k(k为常数),数列公差为d
Sn=(a1+an)n/2=na1+n(n-1)d/2
S2n=2na1+2n(2n-1)d/2=2na1+n(2n-1)d
所以有:
k[2na1+n(2n-1)d]=na1+n(n-1)d/2
d=(4k-2)a1/[(1-4k)n+2k-1]
d应为常数,故与n无关
所以k=1/4,d=-a1/(-1/2)=2a1
an=a1+(n-1)d=(2n-1)a1

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