Sn是首项为a的等比数列{an}的前n项的和,则Sn=a(1-q^n)/(1-q)S3,S9,S6成等差数列,则S9-S3=S6-S9即a[(1-q^9)-(1-q^3)]/(1-q)=a[(1-q^6)-(1-q^9)]/(1-q),q^3-q^9=q^9-q^6,所以q-q^7=q^7-q^4,aq-aq^7=aq^7-aq^4,a2-a8=a8-a5所以a2,a8,a5成等差数列由上面推算过程可知1-q^6=q^6-q^3,2q^6-q^3-1=0,(2q^3+1)(q^3-1)=0,q^3=1或q^3=-1/2Tn=a1+2a4+3a7+...+na(3n-2)=a[1+2q^3+3q^6+...+nq^(3n-3)...
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