Question

设等差数列{an}的前n项和为Sn,等比数列{bn}的前n项和为Tn,已知数列{bn}的公比为q（q＞0）,a1=b1=

Answer 1

1.

S5=5a1+5×4d/2=5+10d=45 10d=40

d=4

an=a1+(n-1)d=1+4(n-1)=4n-3

n=1时,a1=4-3=1,同样满足.(这步判断一定要有)

数列{an}的通项公式为an=4n-3.

T3=b1+b2+b3=b1(1+q+q^2)=1×(1+q+q^2)=1+q+q^2

a3-b2=4×3-3-b1q=9-q

T3=a3-b2

1+q+q^2=9-q,整理,得

q^2+2q-8=0

(q+4)(q-2)=0

q=-4(