已知等差数列{an}的前n项和为Sn,a2=4,S5=35. (Ⅰ)求数列{an}的前n项和Sn; (Ⅱ)若数列{bn}
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已知等差数列{an}的前n项和为Sn,a2=4,S5=35. (Ⅰ)求数列{an}的前n项和Sn; (Ⅱ)若数列{bn}满足bn
已知等差数列{an}的前n项和为Sn,a2=4,S5=35.
(Ⅰ)求数列{an}的前n项和Sn;
(Ⅱ)若数列{bn}满足bn=ean,求数列{bn}的前n项和Tn.
已知等差数列{an}的前n项和为Sn,a2=4,S5=35.
(Ⅰ)求数列{an}的前n项和Sn;
(Ⅱ)若数列{bn}满足bn=ean,求数列{bn}的前n项和Tn.
1.a2=a1+d=4
sn=na1+n(n-1)d/2,即S5=5a1+10d=35
解得 a1=1,d=3∴ Sn=n+ 3n(n-1)/2=n(3n-1)/2
2.bn=e^an=e^(3n-2)
b(n+1)=e^(3n+1)
b(n+1)/bn=e^3
所以bn是等比数列,首项b1=e,公比为e^3
Tn=e(1-e^3n)/(1-e^3)
sn=na1+n(n-1)d/2,即S5=5a1+10d=35
解得 a1=1,d=3∴ Sn=n+ 3n(n-1)/2=n(3n-1)/2
2.bn=e^an=e^(3n-2)
b(n+1)=e^(3n+1)
b(n+1)/bn=e^3
所以bn是等比数列,首项b1=e,公比为e^3
Tn=e(1-e^3n)/(1-e^3)
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