Which of the following is a general recursive formula for the geometric sequence 1, 5, 25, 125, 625, ...?

Question

A. a₁=1, a_n= (1/5)a_n-1

 

B. a₁=1, a_n= 4a_n-1

 

C. a₁=1, a_n= 5a_n-1

 

D. cannot be written in recursive form

Answer 1

A geometric sequence has a common ratio.

 

It may help to first put the sequence into words:

   -  the first value is 1

   -  after the first term, each term is 5 times the previous term

 

The recursive definition is:

    a₁=1 

    a_n= 5a_n-1  for n>1