设{an}是等差数列,{bn}是等比数列,Sn、Tn分别是数列{an}、{bn}的前n项和.若a3=b3,a4=b4,且S5-S3T4-T2=7,则a5b3+b6的值为( ) A.12 B.23 C.57 D.95
问题描述:
设{an}是等差数列,{bn}是等比数列,Sn、Tn分别是数列{an}、{bn}的前n项和.若a3=b3,a4=b4,且
=7,则
S5-S3
T4-T2
的值为( )a5
b3+b6
A.
1 2
B.
2 3
C.
5 7
D.
9 5
答
设等差数列的等差为d,等比数列的等比是q,由a3=b3,得a4-d=b4q,又∵a4=b4,∴a4-a4q=d,∵S5-S3T4-T2=7,∴a5+a4b4+b3=a4+d+a4a4+a4q=7,即3a4-a4qa4+a4q=7,即q=-2.∴a5b3+b6=a5a3+4a4=a4+32a4a4-32a4+4a4=57....