To help Year 9 students understand the nth terms of sequences, here are some simple strategies:

1. Understanding Common Differences:

   • Start by explaining that in an arithmetic sequence, the difference between numbers stays the same.
   • For example, look at the sequence 2, 5, 8, 11. The difference between each number is 3.

2. Finding the nth Term:

   • Teach them how to use a formula to find the nth term:
     • $a_n = a_1 + (n - 1) \cdot d$
     • Here, $a_1$ is the first number in the sequence, and $d$ is the common difference.
   • Using our earlier example:
     • $a_1 = 2$ and $d = 3$, we can plug these values into the formula.
     • So, $a_n = 2 + (n - 1) \cdot 3$.

3. Practice with Examples:

   • Encourage students to create their own sequences and find the nth term.
   • For instance, take the sequence 4, 7, 10, 13. Ask them to find $a_n$.

By exploring and practicing these ideas, students will really understand how to work with sequences!