Question

What is the recursive formula for 1600, 160, 16,.. ?

Answer 1

`a_n=a_{n-1}/10` or, if you prefer, `a_{n+1}=a_n/10`, where `a_0=1600`.

Explanation:

So, the first step is to define your first term, `a_0=1600`. After that, you need to recognize how each term relates to the previous term in the sequence. In this case, every term is decreasing by a factor of `10`, so we get that the following term in the sequence, `a_{n+1}`, is equal the the current term divided by `10`, `a_n/10`. The other representation is simply a change of perspective obtained by looking for a term in the sequence based on the previous one, rather than looking for the next term in the sequence based upon the current one. In essence they say the same thing, though.