设Sn为数列an的前n项和,Sn=kn∧2+n+r,n∈N*,(k是常数).(1)若an为等差数列,求r的值.(2)若r=0且a2m(下标,后同)、a4m、a8m(m∈N*)成等比数列,求k的值.
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![设Sn为数列an的前n项和,Sn=kn∧2+n+r,n∈N*,(k是常数).(1)若an为等差数列,求r的值.(2)若r=0且a2m(下标,后同)、a4m、a8m(m∈N*)成等比数列,求k的值.](/uploads/image/z/5241777-33-7.jpg?t=%E8%AE%BESn%E4%B8%BA%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2CSn%3Dkn%E2%88%A72%2Bn%2Br%2Cn%E2%88%88N%2A%2C%EF%BC%88k%E6%98%AF%E5%B8%B8%E6%95%B0%EF%BC%89.%EF%BC%881%EF%BC%89%E8%8B%A5an%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%B1%82r%E7%9A%84%E5%80%BC.%EF%BC%882%EF%BC%89%E8%8B%A5r%3D0%E4%B8%94a2m%EF%BC%88%E4%B8%8B%E6%A0%87%2C%E5%90%8E%E5%90%8C%EF%BC%89%E3%80%81a4m%E3%80%81a8m%EF%BC%88m%E2%88%88N%2A%EF%BC%89%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E6%B1%82k%E7%9A%84%E5%80%BC.)
设Sn为数列an的前n项和,Sn=kn∧2+n+r,n∈N*,(k是常数).(1)若an为等差数列,求r的值.(2)若r=0且a2m(下标,后同)、a4m、a8m(m∈N*)成等比数列,求k的值.
设Sn为数列an的前n项和,Sn=kn∧2+n+r,n∈N*,(k是常数).(1)若an为等差数列,求r的值.(2)若r=0且a2m(下标,后同)、a4m、a8m(m∈N*)成等比数列,求k的值.
设Sn为数列an的前n项和,Sn=kn∧2+n+r,n∈N*,(k是常数).(1)若an为等差数列,求r的值.(2)若r=0且a2m(下标,后同)、a4m、a8m(m∈N*)成等比数列,求k的值.
a(1)=s(1)=k+1+r,
a(n+1)=s(n+1)-s(n)=k(2n+1)+1=2k(n+1-1) + k+1,
(1),
a(n+1)=2k(n+1-1)+k+1,a(1)=k+1+r.
a(2)=2k(1+1-1)+k+1=2k+k+1,a(1)=k+1+r,
2k=a(2)-a(1)=2k-r,r=0.
(2),
a(1)=k+1,
a(n+1)=2kn+k+1,
a(n)=2k(n-1)+k+1.
[a(4m)]^2=[2k(4m-1)+k+1]^2=a(2m)a(8m)=[2k(2m-1)+k+1][2k(8m-1)+k+1]=[2k(4m-1)+k+1-2k(2m)][2k(4m-1)+k+1+2k(4m)]=[2k(4m-1)+k+1]^2+2k(2m)[2k(4m-1)+k+1]-2k(2m)*(2k)(4m),
0=2k(2m)[2k(4m-1)+k+1] - 32(km)^2
=4km[2k(4m-1)+k+1 - 8km]
=4km[8km-2k+k+1-8km]
=4km[1-k]
0=k[1-k],
k=0或,k=1.