In the sequence 582, 605, 588, 611, 634, 617, 600, which single term is wrong because it does not fit the consistent alternating pattern in the series?

Introduction / Context:
This question is about identifying the wrong term in a numerical series. The sequence here is based on alternating increments and decrements, and you need to detect that underlying rule. Such pattern-detection problems are standard in competitive exams and help assess numerical reasoning ability.

Given Data / Assumptions:
The sequence is: 582, 605, 588, 611, 634, 617, 600. We assume that the sequence is constructed using a simple and regular pattern involving additions and subtractions of fixed numbers. Exactly one term is assumed to be incorrect.

Concept / Approach:
When the numbers fluctuate (go up and down), it is natural to suspect an alternating pattern: for example, adding a fixed number, then subtracting another fixed number, and so on. The key is to compute the differences between consecutive terms and see whether a simple alternation appears.

Step-by-Step Solution:
Step 1: Write the sequence with differences:
582 → 605 (difference +23)
605 → 588 (difference -17)
588 → 611 (difference +23)
611 → 634 (difference +23)
634 → 617 (difference -17)
617 → 600 (difference -17)Step 2: Look for a pattern in the differences. We can see +23, -17, +23, +23, -17, -17.Step 3: A natural clean pattern would be +23, -17, +23, -17, +23, -17 (alternating between +23 and -17).Step 4: Apply the ideal pattern starting from 582: 582 + 23 = 605; 605 - 17 = 588; 588 + 23 = 611; 611 - 17 = 594; 594 + 23 = 617; 617 - 17 = 600.Step 5: In this corrected series the fourth term is 594, not 634. So the term 634 is the wrong value in the given sequence.

Verification / Alternative check:
Notice that with 634 kept as it is, the differences become asymmetric: we have two consecutive +23 steps in the middle (+23 from 588 to 611 and +23 from 611 to 634) and then two consecutive -17 steps at the end. This breaks the neat alternation we derived. Replacing 634 by 594 restores a perfectly regular +23, -17 alternation, confirming that 634 is indeed the outlier.

Why Other Options Are Wrong:
600, 611 and 605 all become consistent members of the series once we enforce the alternate +23 and -17 rule. Changing any of them would force multiple other changes, while changing 634 alone fixes the entire pattern, so those terms cannot be the unique wrong member.

Common Pitfalls:
Candidates may try to fit a more complicated pattern or focus only on local differences without checking the full series. Another error is to accept a pattern that works for only a portion of the sequence. Always look for a simple, global rule that fits all other terms except one.

Final Answer:
The only term that violates the alternating +23 and -17 pattern is 634.