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.

• A. 1
• B. 2
• C. 3
• D. can’t be determined

Answer 1

The correct option is C 3

Let us see the sequence of the numbers:

Number Last term of the number

1 1

2 3

3 6

4 10

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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)