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$1$ $\underline{\text{Recurrence Relations}}$  \vspace{2mm}  Throughout one's education and as one progresses through grade levels, a common math problem that students are faced with are puzzles in which they have to determine what number comes next in a sequence. For example, a teacher may ask a student to fill in the missing number in given  the following problem: following:  \[ 1,4,7,10 \underline{\hspace{1cm}}, ... \]