The missing number in the series 4, 18, ___, 100, 180, 294, 448... is 48.
This series follows a pattern where each number is generated by the formula n * (n+1)², where 'n' represents the position of the number in the series. Let's break it down:
- 1 (1+1)² = 1 2² = 4 (First number in the series)
- 2 (2+1)² = 2 3² = 18 (Second number in the series)
- 3 (3+1)² = 3 4² = 48 (Missing number)
- 4 (4+1)² = 4 5² = 100 (Fourth number in the series)
- 5 (5+1)² = 5 6² = 180 (Fifth number in the series)
- 6 (6+1)² = 6 7² = 294 (Sixth number in the series)
- 7 (7+1)² = 7 8² = 448 (Seventh number in the series)
Multiple sources (Byjus, Quora, Another Quora, Toppr, Testbook, Doubtnut, Another Toppr) confirm this solution. Therefore, the complete series is: 4, 18, 48, 100, 180, 294, 448...
