The pattern you provided is 88, 92, 96, 100.
To investigate the rule for this sequence, let's look at the differences between consecutive numbers:
- 92 - 88 = 4
- 96 - 92 = 4
- 100 - 96 = 4
We can see that each number is increasing by 4.
To express this as a rule or formula, we can start with the first term and add the difference multiplied by the term's position in the sequence. Let \( n \) be the position of the term in the sequence (starting with \( n = 1 \) for the first term):
- The first term (n=1) is 88.
- The second term (n=2) is \( 88 + 4 \times 1 = 92 \).
- The third term (n=3) is \( 88 + 4 \times 2 = 96 \).
- The fourth term (n=4) is \( 88 + 4 \times 3 = 100 \).
In general, we can express the \( n \)-th term of this sequence as:
\[ a_n = 88 + 4(n - 1) \]
Or simplified:
\[ a_n = 84 + 4n \]
This formula can give you any term in the sequence based on its position \( n \). The sequence consists of numbers starting from 88 and increasing by 4 for each subsequent term.