Question 43

A new sequence is obtained from the sequence of positive integers {1,2,3,---} by deleting all the perfect squares. The $$2018^{th}$$ term of the new sequence is

Solution

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Let us write all the number the numbers from 1 to 2018. Here we find that there are 44 numbers that are perfect squares which are 1,4,9... 1936($$44^2$$). Thus after removing the perfect square it has total of 2018-44 = 1974 terms.

Taking next 44 terms from 2019, it will be (2019,2020,2021..... 2062) in which there is 1 perfect square (2025 which is $$45^2$$) hence it is removed and now there is total of 2017 terms. Next term has to be 2063 which is also $$2018^{th}$$ term

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