Question

已知等差数列{an}中,a1=2,a4+a5=25,等比数列{bn}中,b1=a2,b2=a7.

Answer 1

1.

A4=A1+3d

A5=A1+4d

A4+A5=2A1+7d=2×2+7d=25

d=3

Sn=n(A1+An)/2

=n(A1+A1+(n-1)d)/2

=n(2+2+3(n-1))/2

=n(3n+1)/2

2.

B1=A2=A1+d=2+3=5

B2=A7=A1+6d=2+6×3=20

q=B2/B1=20/5=4

Bn=B1×q^(n-1)

=5×4^(n-1)