Question

已知等比数列{an}中,a1+a3=10,前4项和为40 (I)求数列{an)的通项公式； (Ⅱ)若等差数列{bn}的各

Answer 1

1.

A1+A2+A3+A4=40

A2+A4=40-10=30

A2+A4=A1×q+A3×q=10×q=30

q=3

A1+A3=A1×(1+q^2)=10A1=10

A1=1

An=3^(n-1)

2.

A1=1 A2=3 A3=9

T3=3B2=15 B2=5

A2+B2=3+5=8

A1+B1=A1+B2-d=6-d

A3+B3=A3+B2+d=14+d

(A1+B1)×(A3+B3)=(A2+B2)^2

(6-d)(14+d)=64

d^2+8d-20=0

(d+10)(d-2)=0

An>0 d>0

d=2

B1=B2-d=5-2=3

Tn=(B1+Bn)×n/2=(3+3+2(n-1))×n/2=n(n+2)