等差数列{an}的前n项和为Sn,若S2=2,S4=10,则S8=?S15=?S30=?

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等差数列{an}的前n项和为Sn,若S2=2,S4=10,则S8=?S15=?S30=?
等差数列{an}的前n项和为Sn,若S2=2,S4=10,则S8=?S15=?S30=?

等差数列{an}的前n项和为Sn,若S2=2,S4=10,则S8=?S15=?S30=?
2a1+d=2
4a1+6d=10
解得 a1=1/4,d=3/2;
S8=(1/4+1/4+7d)*8/2=44,
S15=(1/4+1/4+14d)*15/2=645/4;
S30=(1/4+1/4+29d)*30/2=660;

s4=a1+a2+a3+a4
=s2+a1+2d+a2+2d
=2s2+4d
10=2*2+4d
4d=6
d=3/2
s2=a1+a1+d
2=2a1+d
2a1=2-3/2
a1=1/4
s8=a1+a2+a3+a4+...+a8
=s4+a1+4d+a2+4d+a3+4d+a4+4d
=2s4+1...

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s4=a1+a2+a3+a4
=s2+a1+2d+a2+2d
=2s2+4d
10=2*2+4d
4d=6
d=3/2
s2=a1+a1+d
2=2a1+d
2a1=2-3/2
a1=1/4
s8=a1+a2+a3+a4+...+a8
=s4+a1+4d+a2+4d+a3+4d+a4+4d
=2s4+16d
=2*10+16*3/2
=20+24
=44
a8=a1+7d
=1/4+7*3/2
=1/4+42/4
=43/4
s15
=(a1+a15)*15/2
=2a8*15/2
=15a8
=15*43/4
=645/4
S30
=2s15+225d
=2*645/4+225*3/2
=645/2+675/2
=660

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