Next Term of the Sequence 18 14 11 9...

The sequence in question is 18, 14, 11, 9, and we are tasked with predicting the next term in the series. To better understand the pattern, let's break it down step by step.

Understanding the Pattern

The sequence starts with the number 18. To get the subsequent terms, the difference between consecutive terms decreases incrementally by 1 each time. Here's a closer look at the pattern:

Difference between the first and second terms: 18 - 14 4 Difference between the second and third terms: 14 - 11 3 Difference between the third and fourth terms: 11 - 9 2

Therefore, the difference between the fourth and next (fifth) terms should be 1 less than 2, which is 1. Thus, the next term is calculated as follows:

Calculation of the Next Term

To find the next term, we subtract the next decrementing number from the previous term in the sequence:

1. Start with the last known term, 9.

2. The decrement for the next term is 1 (since the previous decrement was 2 and it decreases by 1 each time).

9 - 1 8

So, the next term in the sequence is 8.

Generalized Formula

The pattern for the sequence can be generalized as follows:

an an-1 - (n - 6)

Where n is the term number. For the next term (n 5), we have:

a5 a4 - (5 - 6) 9 - (-1) 8

Another Approach: Differences between Consecutive Terms

We can also examine the differences between consecutive terms and observe how they decrease:

Difference between the first and second terms: 18 - 14 4 Difference between the second and third terms: 14 - 11 3 Difference between the third and fourth terms: 11 - 9 2

Following this pattern, the next difference will be 1. Therefore:

11 - 1 8

Conclusion

The next term in the sequence is 8. Understanding the pattern and applying it consistently allows us to predict the next term accurately.

Popular Keywords and Tags

Keywords: sequence, pattern recognition, mathematical sequence
Tags: math, number patterns, sequence analysis, pattern solving, problem-solving