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.
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
Let us see the sequence of the numbers:
Number Last term of the number
11
23
36
410
−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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:
D
Let us see the sequence of the numbers:
Number Last term of the number
11
23
36
410
−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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