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的值设等差数列an的前n项和为sn,若a1=3,s5-s2=27.若sn,2

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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