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To solve this, we are going to use the recursive formula for a geometric sequence: 
where
is the nth term of the geometric sequence.
is the first term of the geometric sequence.
is the common ratio
is the position of the term in the sequence.
We know that the starting salary is $42,000, so
. Now, to find the common ratio , we need to find the next term in the sequence first:
We know from our problem that t<span>he company automatically gives a raise of 3% per year, so the next term in the sequence will be 42000 + 3%(42000) = 42000 + 1260 = 43260. Remember that the common ratio is the current term of the geometric sequence divided by the previous term of the sequence; we know that our current term is 43260 and the previous term is 42000, so:
</span>
<span>Now we can plug the values in our recursive formula:
</span>
We can conclude that the recursive definition for the geometric sequence formed by the salary increase is:
where
We know that the starting salary is $42,000, so
We know from our problem that t<span>he company automatically gives a raise of 3% per year, so the next term in the sequence will be 42000 + 3%(42000) = 42000 + 1260 = 43260. Remember that the common ratio is the current term of the geometric sequence divided by the previous term of the sequence; we know that our current term is 43260 and the previous term is 42000, so:
</span>
<span>Now we can plug the values in our recursive formula:
</span>
We can conclude that the recursive definition for the geometric sequence formed by the salary increase is: