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Question

Consider a sequence of 100 zeroes. It is decided to modify the sequence by following steps. In step 1,to every position in the sequence we add 2 in step 3,to every position in the sequence we add 2.in step 3, to every position which is multiple of 3, we add 2 this is continued up to 100th step after the 100th step what will be the value in 64 th position


Solution

In step 1, to every position 2 is added.
In step 2, to every position which is a multiple of 2 , 2 is added.
In step 3, to every position which is a multiple of 3, 2 is added.
This goes on till 100th step.

So
Step 1 : Every number in the sequence becomes 2

Step 2 : Every number in the sequence is a multiple of 2 (because, every number is a multiple of itself).
So every number in the sequence becomes 4.

Step 3 : Now here, no number is a multiple of 3 since all of them are 4. Thus No change.

Step 4 : Now all the numbers becomes 6. Due to same reason as Step 2.

Step 5 : No change.

Step 6 : All numbers become 8.

This trend continues.
Thus we can see that at each even number Step, 2 is added and at odd number Step, there is no change.
So at 100th step all the numbers become 102.
Hence 64th value , after 100 steps , of the sequence is also 102.

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