an是首项为π/6公差为d的等差数列,且bn=sinan也是等差数列.(1)求公差d (2)若π<d<3π
问题描述:
an是首项为π/6公差为d的等差数列,且bn=sinan也是等差数列.(1)求公差d (2)若π<d<3π
接上 则数列an从第几项开始大于100π(3)求数列bn通项公式
答
(1)b(n-1)+b(n+1)=2bn,a(n-1)+a(n+1)=2an,a(n+1)-a(n-1)=2dsina(n-1)+sina(n+1)=2sinan2sin[a(n-1)+a(n+1)]/2cos[a(n-1)-a(n+1)]/2=2sinan2sinancosd=2sinancosd=1或sinan=0,an=nπ(不符)所以d=2nπ(2)d=2πan=π/6...