Cynthia invests some money in a bank which pays 5% compound interest per year.
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You can observe that every next term is computed by adding 4 to the previous one.
This implies that the difference between consecutive terms is always 4, and this is an arithmetic sequence.
In order to find the explicit equation, we can explore the pattern:
So, as you can see, we have
If 109 is a term of the sequence, there must exist a natural number n such that
So, 109 is not a term of the sequence.