The pattern in the sequence 2, 5, 8, 11 can be described by identifying how each term relates to the previous one.
You can see that each term increases by 3:
- From 2 to 5: \(5 - 2 = 3\)
- From 5 to 8: \(8 - 5 = 3\)
- From 8 to 11: \(11 - 8 = 3\)
Thus, the rule for this pattern is that you start with 2 and add 3 for each subsequent term.
We can express the nth term of the sequence with the formula: \[ a_n = 2 + (n - 1) \cdot 3 \] Where \(a_n\) is the nth term.
This formula can also be simplified to: \[ a_n = 3n - 1 \]
So, the rule defining the pattern is:
- Start with 2, and add 3 for each subsequent term, or through the formula \(a_n = 3n - 1\).