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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.


Options:
A .   0
B .   1
C .   2
D .   3
E .   can’t be determined
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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