The next number in the sequence is 225. This sequence consists of perfect squares: 121, 144, 169, and 196 are all squares of whole numbers. Specifically, 121 is \(11^2\), 144 is \(12^2\), 169 is \(13^2\), and 196 is \(14^2\). Following this logical pattern, the next number should be the square of the next integer, which is 15. Therefore, calculating \(15^2\) gives us 225.
Recognizing patterns in sequences is a crucial skill in competitive exams, and understanding perfect squares can aid in identifying such sequences quickly. In this case, each number represents the square of consecutive integers, making it easier to predict the next in line. When preparing for exams, practicing with similar numerical patterns can enhance problem-solving speed and accuracy.
In summary, identifying the underlying pattern of perfect squares enables us to determine that the next number in this sequence is indeed 225. Familiarity with common mathematical properties, such as squares and other sequences, can significantly improve performance in competitive examinations.
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