已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn...已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn的前n
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![已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn...已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn的前n](/uploads/image/z/729986-50-6.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8D%E5%9B%9B%E9%A1%B9%E5%92%8C%E4%B8%BA10%2C%E4%B8%94a2%2Ca3%2Ca7%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97.%281%29%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan.%EF%BC%882%EF%BC%89%E8%AE%BEbn%3D2%5Ean%2C%E6%B1%82%E6%95%B0%E5%88%97bn...%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8D%E5%9B%9B%E9%A1%B9%E5%92%8C%E4%B8%BA10%2C%E4%B8%94a2%2Ca3%2Ca7%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97.%281%29%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan.%EF%BC%882%EF%BC%89%E8%AE%BEbn%3D2%5Ean%2C%E6%B1%82%E6%95%B0%E5%88%97bn%E7%9A%84%E5%89%8Dn)
已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn...已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn的前n
已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn...
已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn的前n项和Sn
已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn...已知等差数列{an}的前四项和为10,且a2,a3,a7成等比数列.(1)求通项公式an.(2)设bn=2^an,求数列bn的前n
(1)a3^2=a2 a7=(a3-d)(a3+4d)=a3^2+3da3-4d^2
3a3=4d^2
S4=4a3+(-2d-d+d)=4a3-2d=10,a3=(5+d)/2
3(5+d)/2=4d^2
8d^2-3d-15=0
d=(3+/-√489)/16,a3=(83+/-√489)/32
an=a3+(n-3)d
(2)bn=2^(an)代入即得
数列的定义代入就行了
an=3n-5
bn=2^(3n-5)
sn=b1+b2+……
2^3Sn=b2+……
解得sn=1/28*(2^3n-1)
设首项为A1 公差为D:
由前四项和为10得:4A1+6D=10
由A2 43 47成等比得: (A1+2D)平方=(A1+D)(A1+6D)整理得:2D+3A=0
由以上二式解得: A1=-2 D=3
即AN=3N-5
2.
(1)an=3n-5或者an=2.5
(2)sn=6*3^n-6*2^n-12*n+25*n,或者sn=6.25n
有个重要的公式:从1的平方加到2^n的和n*(n+1)*(n+2)/6
an=a3+(n-3)d
a3^2=a2 a7=(a3-d)(a3+4d)=a3^2+3da3-4d^2
3a3=4d^2
S4=4a3+(-2d-d+d)=4a3-2d=10, a3=(5+d)/2
3(5+d)/2=4d^2
8d^2-3d-15=0
d=(3+/-√489)/16, a3=(83+/-√489)/32
an=a3+(n-3)d