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 theremainder 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 theremainder 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
1 1
2 3
3 6
4 10
-- --
N ∑n
We have to find the value of N for the 2000th term. Using iteration we find that if N = 62, the last term that ends with N is (1/2* 62 * 63) = 1953.
Therefore, the next 63 terms are 63. So the 2000th term is 63. So the remainder is 3. Hence option (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
We have to find the value of N for the 2000th term. Using iteration we find that if N = 62, the last term that ends with N is (1/2* 62 * 63) = 1953.
Therefore, the next 63 terms are 63. So the 2000th term is 63. So the remainder is 3. Hence option (d)
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