问题
解答题
已知等差数列{an}的前n项和为Sn,且a4-a2=4,S5=30等比数列{bn}中,bn+1=3bn,n∈N+,b1=3.
(1)求an,bn;
(2)求数列{an•bn}的前n项和Tn.
答案
(1)等差数列{an}中,∵a4-a2=4,∴2a=4,∴d=2
∵S5=30,∴5a1+10d=30,∴a1=2
∴an=2n;
等比数列{bn}中,bn+1=3bn,b1=3,∴bn=3•3n-1=3n;
(2)Tn=2•31+4•32+…+2n•3n
∴3Tn=2•32+4•33+…+(2n-2)•3n+2n•3n+1
两式相减可得-2Tn=2•31+2•32+4•32+…+2•3n-2n•3n+1=-3-(2n-1)•3n+1
∴Tn=
•3n+1+2n-1 2
.3 2