数列an中sn=3n^2+5n在数列bn中,b1=8,64bn+1-bn=0常数c,使对任意的正整数n,an+logcbn值为m,求c和m

数列an中sn=3n^2+5n在数列bn中,b1=8,64bn+1-bn=0常数c,使对任意的正整数n,an+logcbn值为m,求c和m
数列an中sn=3n^2+5n在数列bn中,b1=8,64bn+1-bn=0常数c,使对任意的正整数n,an+logcbn值为m,求c和m

数列an中sn=3n^2+5n在数列bn中,b1=8,64bn+1-bn=0常数c,使对任意的正整数n,an+logcbn值为m,求c和m
an=sn-s(n-1)=3n^2-3(n-1)^2+5=3(2n-1)+5=6n+2,
bn=8*(1/64)^(n-1)=8^(3-2n),
an+logcbn=6n+2+logc8^(3-2n)=6n+2+(3-2n)logc8,
an+logcbn=m为常数,故6n-2nlogc8=0,logc8=3,c=2,
m=2+3*3=11