A sequence is made by following the rules below. What is the 300th term in the sequence?
(Hint: write out the sequence until you notice a pattern.)
- The first term is 3
- If a term is even, divide it by 2 to get the next term
- If a term is odd, multiply it by 3 then add 1 to get the next term

Step 1 ：Let's denote the sequence as $a_n$, where $n$ is the term number. So $a_1 = 3$.

Step 2 ：Let's write out the first few terms of the sequence to see if we can find a pattern: $a_1 = 3$, $a_2 = 3*3+1 = 10$, $a_3 = 10/2 = 5$, $a_4 = 5*3+1 = 16$, $a_5 = 16/2 = 8$, $a_6 = 8/2 = 4$, $a_7 = 4/2 = 2$, $a_8 = 2/2 = 1$, $a_9 = 1*3+1 = 4$, $a_{10} = 4/2 = 2$, $a_{11} = 2/2 = 1$, $a_{12} = 1*3+1 = 4$, $a_{13} = 4/2 = 2$, $a_{14} = 2/2 = 1$, $a_{15} = 1*3+1 = 4$.

Step 3 ：We can see that starting from $a_8$, the sequence enters a loop of 4-2-1. This loop repeats indefinitely.

Step 4 ：Since the 300th term is in the loop, we can find its position in the loop by taking the remainder when 300 is divided by the length of the loop. The length of the loop is 3, so the position of the 300th term in the loop is $300 \mod 3 = 0$.

Step 5 ：Since the remainder is 0, the 300th term is the same as the last term in the loop, which is 1.

Step 6 ：So, the 300th term of the sequence is \(\boxed{1}\).