设等差数列an的前n项和为sn,若a1=3,s5-s2=27.若sn,2√2(an+1+1),sn+2成等比数列,求正整数n的值
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![设等差数列an的前n项和为sn,若a1=3,s5-s2=27.若sn,2√2(an+1+1),sn+2成等比数列,求正整数n的值](/uploads/image/z/370164-12-4.jpg?t=%E8%AE%BE%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%2C%E8%8B%A5a1%3D3%2Cs5-s2%3D27.%E8%8B%A5sn%2C2%E2%88%9A2%28an%2B1%2B1%29%2Csn%2B2%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E6%B1%82%E6%AD%A3%E6%95%B4%E6%95%B0n%E7%9A%84%E5%80%BC)
设等差数列an的前n项和为sn,若a1=3,s5-s2=27.若sn,2√2(an+1+1),sn+2成等比数列,求正整数n的值
设等差数列an的前n项和为sn,若a1=3,s5-s2=27.若sn,2√2(an+1+1),sn+2成等比数列,求正整数n的值
设等差数列an的前n项和为sn,若a1=3,s5-s2=27.若sn,2√2(an+1+1),sn+2成等比数列,求正整数n的值
an= a1+(n-1)d = 3+(n-1)d
S5-S2= 27
(a1+2d)5 -(2a1+d) =27
3a1+9d=27
9d=18
d=2
an = 3+2(n-1)= 2n+1
Sn,2√2(a(n+1)+1),S(n+2)成等比数列
Sn.S(n+2) = 8(a(n+1)+1)^2
[(n+2)n].[(n+2)(n+4)] = 8(2n+4)^2
(n+2)^2.( n^2+4n-32) =0
(n+2)^2.(n+8)(n-4)=0
n=4
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