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A new sequence is obtained from the sequence of positive integers (1, 2, 3…) by deleting all the perfect squares. The 2018 term of the new sequence is 


1. 2061
2. 2062
3. 2063
4. 2065

1 Answer

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Best answer
Correct Answer - Option 3 : 2063

Calculation:

A perfect square near a natural number can be done by the hit and trial method unless it is a large number with more than 4 digits.

⇒ Original sequence : 1, 2, 3, 4, 5, 6, ...... 

⇒ New sequence : 2, 3, 5, 6, 7, 8, 10, ........

⇒ Thus before 2018, there are 44 perfect squares (442 = 1936).

⇒ Thus 44 numbers will be missing in the new sequence compared to the original, thus the 2018th number will be 2018 + 44 = 2062.

⇒ Students often tend to mistake here by ticking 2062.

⇒ [452 = 2025] will be included in the new sequence too, thus 2062 + 1 = 2063 is the correct answer.

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