Question

What is a possible explicit rule for the nth term of the sequence: `25, 15, 5, -5, -15`?

Answer 1

`a_n = 25-10(n-1)`

Explanation:

An arithmetic sequence is a sequence in which there is a constant difference between successive terms. Given an arithmetic sequence with initial term `a_1` and a constant difference `d` we can write the `n^"th"` term as `a_n = a_1+d(n-1)`

In this case, as each term is `10` less than the previous term, the sequence is potentially an arithmetic sequence with initial term `25` and constant difference `-10`, meaning we would have `a_n = 25 -10(n-1)`