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Answer:
The sequence 2, 4, 7, 11, ... can be described by the rule of adding an incrementally increasing integer to the previous term. Here's how it works:
- Start with 2.
- Add 2 to get the next term: \( 2 + 2 = 4 \).
- Add 3 to the previous term (4) to get the next term: \( 4 + 3 = 7 \).
- Add 4 to the previous term (7) to get the next term: \( 7 + 4 = 11 \).
So, the sequence follows the rule:
\[ a_n = a_{n-1} + n \]
where \( a_1 = 2 \) and \( n \) is the position in the sequence starting from 2.
To find the next term, add 5 to the previous term (11):
\[ 11 + 5 = 16 \]
Therefore, the sequence continues with 2, 4, 7, 11, 16, ...