Understanding Sequence Patterns: Uncovering the Missing Number in 15 30 45 60 ___

The 15 30 45 60 ___ sequence is a classic example of an arithmetic pattern. An arithmetic sequence is a series of numbers where the difference between consecutive terms is constant. In this particular sequence, each term is 15 more than the previous one.

Identifying the Pattern

Let's break down the sequence step-by-step to understand why the missing number is 75.

The Sequence: 15 30 45 60 75

The sequence starts with 15, and each subsequent number is 15 more than the last. Following the pattern, we add 15 to 60 to find the missing number:

Starting with 15, we add 15 to get 30. Adding 15 to 30 gives us 45. Adding 15 to 45 results in 60. To find the next number, we add 15 to 60: 60 15 75.

Thus, the missing number in the sequence is 75.

Why 75?

Each term in the sequence is a multiple of 15. The sequence follows a clear arithmetic rule where each number is obtained by adding 15 to the previous one. Hence, the next number is derived by continuing this pattern.

Another way to verify this is by looking at the pattern:

15 15 15 30 30 15 45 45 15 60 60 15 75

Other Sequence Patterns

While the sequence 15 30 45 60 75 is clear, other sequences might have different patterns or steps.

Example: 15 30 25 45 90

This sequence follows a different pattern:

15 (First term) 30 (Second term, 15 15) 25 (Third term: 30 - 5) 45 (Fourth term, 25 20) 90 (Fifth term, 45 45)

In this case, the missing term is 3030, which fits the pattern where alternating terms increase and decrease by a certain value.

Conclusion

The sequence 15 30 45 60 ___ has a simple and consistent pattern where each term increases by 15. Understanding such patterns is crucial for solving various sequence-based problems. Whether it's an arithmetic series or a more complex pattern, identifying the underlying rule helps in predicting the missing number.

For more help with sequence problems or to explore similar patterns, refer to the table of 15 or seek additional examples in pattern recognition exercises.