The pattern given consists of the numbers 75, 70, 65, and 60. To find the rule governing this sequence, let's look at the differences between consecutive numbers:
- 75 to 70: \( 75 - 70 = 5 \)
- 70 to 65: \( 70 - 65 = 5 \)
- 65 to 60: \( 65 - 60 = 5 \)
We can see that each number decreases by 5. This shows a consistent pattern: each term in the sequence is 5 less than the previous term.
The rule for this pattern can be expressed as:
- \( a_n = a_{n-1} - 5 \), where \( a_1 = 75 \).
If we were to extend this pattern, the next number would be:
- \( 60 - 5 = 55 \)
Thus, the sequence continues as 75, 70, 65, 60, 55, and so on, decreasing by 5 each time.