Question

已知等比数列{an},Sn是其前n项和,且a1+a3=5,S4=15,设bn=(5/2)+log2(an),求数列{bn

Answer 1

S4=a1+a2+a3+a4=a1+a3+q(a1+a3)=15

5+5q=15

q=2

a1+a3=5

a1+aq^2=5

a1+4a1=5

a1=1

an=a1q^n-1

=2^n-1

b1=5/2

b2=5/2+1

bn=（5/2）+log2(an),

=5/2+2^n-1

Tn=5/2+5/2+0+1+.+5/2+2^n-1

=5/2*n+0+1+2+.+2^n-1

=5n/2+(1-2^n)/(1-2)

=5n/2+2^n-1