Complete the series 2, 5, 9, 19, 37.......(A) 55(B) 65(C) 85(D) 75
Question
Complete the series 2, 5, 9, 19, 37.......(A) 55(B) 65(C) 85(D) 75
Solution
The pattern in the series is as follows:
- 2 to 5: Add 3
- 5 to 9: Add 4
- 9 to 19: Add 10
- 19 to 37: Add 18
If we look closely, the numbers we are adding are also following a pattern: 3, 4, 10, 18. Each of these numbers is one less than a perfect square: 4 (2^2), 5 (3^2 - 1), 9 (4^2 - 1), 16 (5^2 - 1).
So, the next number to add would be one less than the next perfect square, which is 6^2 - 1 = 35.
Adding 35 to the last number in the series (37) gives us 72.
However, none of the options (A) 55, (B) 65, (C) 85, (D) 75 match this result. There might be a mistake in the question or the options provided.
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