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Find the missing number: 1, 4, 9, 16, 25, ?
30
35
36
40
36
Identify the series as the sequence of perfect squares of consecutive natural numbers (n²).
Identify the series as the sequence of perfect squares of consecutive natural numbers (n²).
Analyze the number pattern
Observe the terms: 1, 4, 9, 16, 25. These are squares of natural numbers starting from 1: 1 squared = 1, 2 squared = 4, 3 squared = 9, 4 squared = 16, 5 squared = 25.
Determine the next term
The pattern follows the square of the next natural number, which is 6. Calculating 6 squared gives 6 multiplied by 6, which equals 36.
A: 30 is not a perfect square and does not follow the n² pattern. B: 35 is not a perfect square. D: 40 is not a perfect square and follows no logical progression in this series.
C is correct because the series represents the squares of consecutive natural numbers (1 squared, 2 squared, 3 squared, 4 squared, 5 squared), making the next term 6 squared, which is 36.
For any numeric series, always check for squares, cubes, or prime numbers first, as these are the most common patterns in competitive exams.
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