Find out the wrong number in the given sequence of numbers. 582, 605, 588,…

Concept: In an alternating-difference number series, consecutive terms do not share one constant difference; instead two operations repeat in a fixed order — here, add 23, then subtract 17, alternating throughout. To find the wrong term, rebuild the sequence from the first term using this rule and compare it, term by term, with the given sequence; the term where they diverge is the wrong number.

1. Apply the rule from the first term: 582 + 23 = 605, 605 - 17 = 588, 588 + 23 = 611, 611 - 17 = 594, 594 + 23 = 617, 617 - 17 = 600.

2. This gives the expected sequence: 582, 605, 588, 611, 594, 617, 600.

3. Compare it with the given sequence: 582, 605, 588, 611, 634, 617, 600.

4. Every term matches except the fifth position: the rule gives 594, but the given sequence shows 634.

Cross-check: continuing the rule from the corrected value 594 gives 594 + 23 = 617 and 617 - 17 = 600, which matches the sixth and seventh given terms exactly. This confirms 634 is the sole term that breaks the pattern.