Question
Consider the non-decreasing sequence of positive integers:
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5.... in which nth positive number appears n times. Find the remainder when the 2000th term is divided by 4.
Answer: Option D
:
D
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:
D
Let us see the sequence of the numbers:
Number Last term of the number
1 1
2 3
3 6
4 10
−n −n(n+1)2
We have to find the value of n for the 2000th term.
If n = 62, the last term that ends with n is (12×62×63) = 1953.
Therefore, the next 63 terms are 63. So the 2000th term is 63. So the remainder when divided by 4 is 3.
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