5an,5bn,5an+1成等比,lgbn,lgan+1,lgbn+1成等差a1=1 b1=1,b2=3,求an,bn
问题描述:
5an,5bn,5an+1成等比,lgbn,lgan+1,lgbn+1成等差a1=1 b1=1,b2=3,求an,bn
答
由于题上的标签不是很清楚,暂且把n和n+1认为是a 的下标!
5an,5bn,5an+1成等比数列 ,有bn:an=an+1:bn
lgbn,lgan+1,lgbn+1成等差数列,有an+1:bn=bn+1:an+1
所以可有 bn:an=bn+1:an+1 也即是 an:an+1=bn:bn+1
b2:b1=3,an bn均为以1为首项3为比的等比数列
即可求出an=bn=3^(n-1)