Identifying the Pattern and Value of X in the Sequence: 7, 14, 21, X, 35

Introduction

In this article, we will discuss a numerical sequence and identify the value of X. The sequence is: 7, 14, 21, X, 35. We will explore different methods to determine the value of X, including arithmetic progression and multiplication patterns.

Arithmetic Progression Method

The sequence 7, 14, 21, X, 35 can be viewed as an arithmetic progression. In an arithmetic progression, the difference between consecutive terms is constant. Here, the common difference is 7. We can use the formula for the nth term of an arithmetic sequence to find X.

The general formula for the nth term of an arithmetic sequence is:

an a1 (n - 1) d

Where:

a1 is the first term (7), d is the common difference (7), n is the term number.

To find the 5th term (X), we use:

a5 7 (5 - 1) 7

a5 7 4 7 7 28 35

The term before 35 is:

a4 7 (4 - 1) 7

a4 7 3 7 7 21 28

Multiplication Pattern Method

Another way to identify the sequence is through multiplication. Each term is a multiple of 7:

Following this pattern, we can see that 28 is the correct value of X since:

28 7 × 4

Verification with Stepwise Calculation

Let's verify the value of X using an explicit step-by-step calculation:

Step 1: Identify the pattern

The sequence can be written as:

7, 14, 21, X, 35

Each number is a consecutive multiple of 7:

7×1, 7×2, 7×3, 7×4, 7×5

Thus, the next term (7×4) is X, which equals 28.

Conclusion

In conclusion, the value of X in the sequence 7, 14, 21, X, 35 is 28. This can be determined both through arithmetic progression and multiplication patterns. Understanding patterns and using mathematical formulas can help in identifying the missing or next terms in a sequence.

Keywords

sequence analysis, arithmetic progression, multiplication pattern