Question

Let a sequence have 1,000 zeroes. In step 1 we add 2 to every position. In step 2 we add 2 to every even position. In step 3 every position that is a multiple of 3, we add 2. This is continued up to the thousandth step. After 1,000th step what is the value of the 600th position

Answer 1

In step 1:
2 is added to every position.
Therefore the value of 600th position is 2

In step 2:
2 is added to every even position.
Since 600th is an even position,
The value of 600th position is 2+2

In step 3:
2 is added to every position which is a multiple of 3.
Since 600 is a multiple of 3,
The value of 600th position is 2+2+2

Now these steps are continued 1000 times
Therefore value of 600th position is (2+2+2)×1000 i.e 6000