## Pascal 2023 Part C - Question 21, CEMC UWaterloo

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#### Difficulty: 5

#### This problem is tagged with pascal, pascal23, highschool.

**(Pascal 2023, Part C, Question 21, CEMC - UWaterloo)**

Starting with a positive integer $m$, Alicia creates a sequence by applying the following algorithm:

• Step $1$: Alicia writes down the number $m$ as the first term of the sequence.

• Step $2$: If $m$ is even, Alicia sets $n = \frac{1}{2}m$. If $m$ is odd, Alicia sets $n = m + 1$.

• Step $3$: Alicia writes down the number $m+n+1$ as the next term of the sequence.

• Step $4$: Alicia sets $m$ equal to the value of the term that she just wrote down in Step $3$.

• Step $5$: Alicia repeats Steps $2$, $3$, $4$ until she has five terms, at which point she stops.

For example, starting with $m = 1$, Alicia's sequence would be $1$, $4$, $7$, $16$, $25$.

Alicia starts a sequence with $m = 3$. What is the fifth term of her sequence?

*Answer Submission Note(s)*

Your answer should be an integer from 0 to 99, inclusive.

Do NOT code a single digit answer with a leading zero, as you would in the actual contest.

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