已知数列(log3an)是公差为一的等差数列,且a2+a4+a6=9求log1/3(a5+a7+a9)
问题描述:
已知数列(log3an)是公差为一的等差数列,且a2+a4+a6=9求log1/3(a5+a7+a9)
答
(log3an)是公差为一的等差数列
即
log3an=log3a(n-1)+1
log3an=log3a(n-1)+log3(3)
an=3a(n-1)
log1/3(a5+a7+a9)
=log1/3 3^3*(a2+a4+a6)
=log1/3 3^3*9
=log1/3 3^5
=-5