- 数列填空题，求解1.等比数列前n项和Sn=2·(1/3)^n+k
- 1.等比数列前n项和Sn=2·(1/3)^n+k,则常数k的值为________
2.{an}是等差数列，若a1,a3,a4是等比数列{bn}的连续三项，则{bn}的公比为_________
请给出详细的解答过程，谢谢
- 1.a1=S1=2/3+k,
n>1时an=Sn-S=2*(1/3)^n-2*(1/3)^(n-1)
=-4*(1/3)^n,
公比=1/3=a2/a1=(-4/9)/(2/3+k),
∴2/3+k=-4/3,
k=-2.
2.a1,a3,a4是等比数列{bn}的连续三项,
<==>(a1+2d)^2=a1(a1+3d),其中d是公差，
<==>a1d+4d^2=0,
<==>d=0,或a1=-4d.
d=0时公比q=1;a1=-4d时，q=a3/a1=(-2d)/(-4d)=1/2.