已知数列{an}是等差数列,数列{bn}是等比数列,a1=b1=1,若cn=an+bn,且c2=6,c3=11,求数列{cn}的前n项

2024-11-11 23:40:23
推荐回答(1个)
回答1:

设数列{an}、{bn}的公差、公比分别为d、q,

c2=6
c3=11
(1+d)+q=6
(1+2d)+q2=11

消去d得q2-2q=0,∵q≠0,∴q=2,∴d=3,
∴an=3n-2,bn=2n-1
∴Sn=(a1+a2+…+an)+(b1+b2+…+bn
=
n(a1+an
2
+
b1(1?qn)
1?q

=
n(3n?1)
2
+2n-1.