已知数列{an}是等差数列,且bn=an+a(n-1),求证bn也是等差数列

问题描述:

已知数列{an}是等差数列,且bn=an+a(n-1),求证bn也是等差数列

设an=a1+(n-1)d,
bn=an+a(n-1)
=a1+(n-1)d+a1+nd
=2a1+(2n-1)d
bn为首项为2a1-d,公差为2d的等差数列