SOLUTION: Please help... If {b n} is an arithmetic sequence, explain why {10^bn} must be geometric. Thank you.

To prove that the sequence  is a geometric progression, consider the ratio  .

Since   is an AP, you have   = ,  where d is the common difference of the AP, i.e. the constant term independent on "n'.


Therefore,   =  =  = .


Thus the ratio of two consecutive terms   and    is the constant value  .


By the definition, it means that the sequence     is a geometric progression.