First we need to find what kind of sequence we have. To do that we are going to test if the sequence as a difference
, in which case it will be an arithmetic sequence, or a ratio
, in which case it will be geometric sequence.
The formula to find
is
where
is the current term in the sequence
is the previous term in the sequence
The formula to find
is
where
is the current term in the sequence
is the previous term in the sequence
- For
and
- For
and
:
Since
is equal in both procedures whereas
is not, we can conclude that our sequence is an arithmetic sequence.
Now we are going to use the explicit formula of an arithmetic sequence
where
is the nth term
is the first term
is the position of the term in the sequence
is the difference
We know that
and
, so lets replace those values in our formula:
We can conclude that the correct answer is <span>
D) an = 3n - 5</span>