已知等比数列an中2a4-3a3+a2=0,a1=64,公比q不等于1,(1)求An(2)设bn=log2an求数列bn的前n项和tn

Question

已知等比数列an中2a4-3a3+a2=0,a1=64,公比q不等于1,
(1)求An(2)设bn=log2an求数列bn的前n项和tn

Answer 1

(1)
2a4-3a3+a2=0
2a2q^2-3a2q+a2=0
2q^2-3q+1=0
(q-1)(2q-1)=0
q=1(与已知矛盾,舍去)或q=1/2
an=a1q^(n-1)=64×(1/2)^(n-1)=1/2^(n-7)
(2)
bn=log2(an)=log2[1/2^(n-7)]=log2[2^(7-n)]=7-n
Tn=b1+b2+...+bn
=7n-(1+2+...+n)
=7n-n(n+1)/2
=-n^2/2 +13n/2