已知Sn为等差数列an前N项和,若S1=1,S4/S2=4,则S6/S4的值为
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已知Sn为等差数列an前N项和,若S1=1,S4/S2=4,则S6/S4的值为
已知Sn为等差数列an前N项和,若S1=1,S4/S2=4,则S6/S4的值为
已知Sn为等差数列an前N项和,若S1=1,S4/S2=4,则S6/S4的值为
解;
S1=a1=1
Sn为等差数列an前N项和
Sn=a1n+n(n-1)d/2
S4=4+6d
S2=2+d
S4/S2=(4+6d)/(2+d)=4
解得:d=2
S4=4+6d=16
S6=6+15d=36
S6/S4=36/16=9/4
已知Sn为等差数列an前N项和,所以Sn=na1+n(n-1)d/2;因S1=1,所以S1=a1+0=1,则a1=1;因S4/S2=4 ,则 (4a1+4(4-1)d/2)/(2a1+2(2-1)d/2)=4,所以d= 2a1=2 ;
故S6/S4=(6+6(6-1)2/2)/(4+4(4-1)2/2)=36/16=9/4
9/4
a1=1
S4/S2=4
S4=4S2
4a1+6d=4(2a1+d)
2d=4a1
d=2a1=2
所以
S6/S4=(6a1+15d)/(4a1+6d)=36/16=9/4
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