设数列{an}满足:a1=1,an+1=3an,n∈N+.
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设数列{an}满足:a1=1,an+1=3an,n∈N+.
(Ⅰ)求{an}的通项公式及前n项和Sn;
(Ⅱ)已知{bn}是等差数列,Tn为前n项和,且b1=a2,b3=a1+a2+a3,求T20.
(Ⅰ)求{an}的通项公式及前n项和Sn;
(Ⅱ)已知{bn}是等差数列,Tn为前n项和,且b1=a2,b3=a1+a2+a3,求T20.
(Ⅰ)由题意可得数列{an}是首项为1,公比为3的等比数列,
故可得an=1×3n-1=3n-1,
由求和公式可得Sn=
1×(1−3n)
1−3=
1
2(3n−1);
(Ⅱ)由题意可知b1=a2=3,b3=a1+a2+a3=1+3+9=13,
设数列{bn}的公差为d,可得b3-b1=10=2d,解得d=5
故T20=20×3+
20×19
2×5=1010
故可得an=1×3n-1=3n-1,
由求和公式可得Sn=
1×(1−3n)
1−3=
1
2(3n−1);
(Ⅱ)由题意可知b1=a2=3,b3=a1+a2+a3=1+3+9=13,
设数列{bn}的公差为d,可得b3-b1=10=2d,解得d=5
故T20=20×3+
20×19
2×5=1010
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