In the series 5, 16, 6, 16, 7, 16, 9, which one number is wrong because it breaks the pattern of alternating 16 with consecutive integers?

Introduction / Context:
This series question is built on a very straightforward alternating pattern. The number 16 appears repeatedly in every second position, while the other positions contain consecutive integers. You are asked to find out which term does not follow this simple rule.

Given Data / Assumptions:
The sequence is: 5, 16, 6, 16, 7, 16, 9. We assume that 16 is intended to appear at every alternate position, and that the non-16 terms should form a sequence of consecutive integers. One term is incorrect.

Concept / Approach:
When one number is repeated at fixed intervals in a series, it is sensible to separate the series into two subseries: one for the repeated value and one for the changing values. Here, 16 repeats regularly in the 2nd, 4th and 6th positions, so we focus on the 1st, 3rd, 5th and 7th terms to check whether they form a simple pattern like consecutive numbers.

Step-by-Step Solution:
Step 1: Write the sequence with positions: (1) 5, (2) 16, (3) 6, (4) 16, (5) 7, (6) 16, (7) 9.Step 2: Observe the terms in even positions: 16, 16, 16. These are all equal, so they are consistent.Step 3: Now examine the odd-position terms: 5 (position 1), 6 (position 3), 7 (position 5), 9 (position 7).Step 4: We can see that 5, 6 and 7 are consecutive integers. The natural continuation would be 8 as the next consecutive number, not 9.Step 5: Therefore, the last term in the sequence should be 8 to continue the consecutive integer pattern, and the given value 9 is incorrect.

Verification / Alternative check:
If we reconstruct the ideal series, it would be: 5, 16, 6, 16, 7, 16, 8. This has the repeated value 16 at every alternate position and the non-16 terms 5, 6, 7, 8 forming a simple consecutive integer sequence. In the given series, only the last odd-position term (9) breaks this rule, confirming that it is the wrong number.

Why Other Options Are Wrong:
6 and 7 both keep the consecutive pattern alive and are placed correctly between the 16s. The value 16 itself is consistently placed in positions 2, 4 and 6, so it also fits the pattern. Only 9 fails to continue the sequence 5, 6, 7, 8 and therefore stands out as the error.

Common Pitfalls:
Some test-takers may focus on the differences between adjacent terms rather than noticing the alternating structure. They may try to apply a single rule to the entire series, which looks irregular. Recognizing the two interleaved subseries is the key insight for solving this type of question quickly.

Final Answer:
The term that breaks the alternating 16 and consecutive integer pattern is 9.