设等差数列{an}的前n项和为Sn,且a2=2,s4=14.求{an}的通项公式接上 (1)求{an}的通项公式.(2)若不等式2Sn+8n+27大于(-1)nK(an+4) 对所有的正整数n都成立,求实数k的取值范围
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![设等差数列{an}的前n项和为Sn,且a2=2,s4=14.求{an}的通项公式接上 (1)求{an}的通项公式.(2)若不等式2Sn+8n+27大于(-1)nK(an+4) 对所有的正整数n都成立,求实数k的取值范围](/uploads/image/z/1819422-54-2.jpg?t=%E8%AE%BE%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94a2%3D2%2Cs4%3D14.%E6%B1%82%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E6%8E%A5%E4%B8%8A+%EF%BC%881%EF%BC%89%E6%B1%82%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F.%282%29%E8%8B%A5%E4%B8%8D%E7%AD%89%E5%BC%8F2Sn%2B8n%2B27%E5%A4%A7%E4%BA%8E%28-1%29nK%28an%2B4%29+%E5%AF%B9%E6%89%80%E6%9C%89%E7%9A%84%E6%AD%A3%E6%95%B4%E6%95%B0n%E9%83%BD%E6%88%90%E7%AB%8B%2C%E6%B1%82%E5%AE%9E%E6%95%B0k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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设等差数列{an}的前n项和为Sn,且a2=2,s4=14.求{an}的通项公式接上 (1)求{an}的通项公式.(2)若不等式2Sn+8n+27大于(-1)nK(an+4) 对所有的正整数n都成立,求实数k的取值范围
设等差数列{an}的前n项和为Sn,且a2=2,s4=14.求{an}的通项公式
接上 (1)求{an}的通项公式.(2)若不等式2Sn+8n+27大于(-1)nK(an+4) 对所有的正整数n都成立,求实数k的取值范围
设等差数列{an}的前n项和为Sn,且a2=2,s4=14.求{an}的通项公式接上 (1)求{an}的通项公式.(2)若不等式2Sn+8n+27大于(-1)nK(an+4) 对所有的正整数n都成立,求实数k的取值范围
答:
等差数列An,A2=2,S4=14
An=A1+(n-1)d
A2=A1+d=2
S4=A1+A2+A3+A4=4A1+(1+2+3)d=4A1+6d=14
联立上两式解得:A1=-1,d=3
所以:An=-1+3(n-1)=3n-4
所以:An=3n-4
2Sn+8n+27>(-1)nk(An+4)恒成立
Sn=(A1+An)/2=(-1+3n-4)n/2=(3n-5)n/2
(3n-5)n+8n+27>-kn*3n=-3kn^2
3n^2+3n+27>-3kn^2
3(k+1)n^2+3n+27>0恒成立
显然,k+1>=0
所以:k>=-1
(1)s4=14
a1+a2+a3+a4=14
a2+2a2+a2+2d=14
4a2+2d=14
8+2d=14
d=3
a2=a1+d=a1+3=2
a1=-1
an=-1+3(n-1)=3n-4
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