Identifying the Misplaced Number in the Series: 7 13 19 26 31 37 43

Sequences and series are fundamental concepts in mathematics, and one common type of problem is identifying a misplaced number in a given series. This article aims to explore the series 7 13 19 26 31 37 43 and determine which number is incorrect. Furthermore, we will provide a detailed breakdown of the reasoning behind the solution.

A Series Discrepancy

The series in question is 7 13 19 26 31 37 43. To determine the erroneous number, we need to examine the differences between consecutive terms:

7 6 13 13 6 19 19 6 26 26 6 32 (instead of 31) 31 6 37 37 6 43

The pattern appears to be consistent, with each term being 6 more than the previous term. Therefore, we can deduce that the discrepancy occurs between 19 and 26.

The Corrected Series

Given the consistent pattern, the correct series should be:

7 13 19 25 (instead of 26) 31 37 43

With this corrected series, each term follows the pattern of adding 6 to the previous term.

A Mathematical Formula

To generalize, we can express the nth term of the corrected series as:

an a1 (n-1)6

Where:

an is the nth term of the series a1 is the first term (7 in this case) n is the position of the term in the series

Using the formula, we can verify each term:

a1 7 a2 13 a3 19 a4 25 a5 31 a6 37 a7 43

Conclusion

Therefore, the number "26" in the series is incorrect, and the correct number is "25". This analysis aligns with the observed pattern that each term is 6 more than the previous term.

Keywords: series analysis, number pattern, sequence discrepancy