设数列{an}是首项为a1(a1>0),公差为2的等差数列,其前n项和为Sn,且根号S1,S2,S
设数列{an}是首项为a1(a1>0),公差为2的等差数列,其前n项和为Sn,且根号S1,S2,S3成等差数列。求数列{an}的通项公式...
设数列{an}是首项为a1(a1>0),公差为2的等差数列,其前n项和为Sn,且根号S1,S2,S3成等差数列。求数列{an}的通项公式
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Sn=a1n+n(n-1)2/2=a1n+n(n-1)
2根号S2=根号S1+根号S3
2根号(2a1+2)=根号a1+根号(3a1+6)
4(2a1+2)=a1+3a1+6+2根号a1(3a1+6)
8a1+8=4a1+6+2根号a1(3a1+6)
4a1+2=2根号a1(3a1+6)
2a1+1=根号a1(3a1+6)
4a1^2+4a1+1=3a1^2+6a1
a1^2-2a1+1=0
(a1-1)^2=0
a1=1
an=a1+(n-1)d=1+(n-1)2=2n-1
2根号S2=根号S1+根号S3
2根号(2a1+2)=根号a1+根号(3a1+6)
4(2a1+2)=a1+3a1+6+2根号a1(3a1+6)
8a1+8=4a1+6+2根号a1(3a1+6)
4a1+2=2根号a1(3a1+6)
2a1+1=根号a1(3a1+6)
4a1^2+4a1+1=3a1^2+6a1
a1^2-2a1+1=0
(a1-1)^2=0
a1=1
an=a1+(n-1)d=1+(n-1)2=2n-1
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