Question

Convert the recursive equation that is below into an explicit equation where a is the initial value and the time elapsed is 1 year.

Answer 1

Answer:

  f(n) = a+200(n -1)

Step-by-step explanation:

The constant difference between terms indicates the sequence is an arithmetic one. The explicit formula for an arithmetic sequence is ...

 an = a1 + d(n -1)

where a1 is the first term and d is the common difference.

Your first term is "a", and your common difference is 200, so the n-th term of the sequence is ...

  an = a + 200(n -1)

Written as a function of n, this is ...

  f(n) = a + 200(n -1)

_____

Based on the problem description, we cannot tell how n relates to time, so we have created an f(n) that gives the same result as the recursive definition of f(n).