srikanthb.69 wrote:Option 1 it clearly shows the sequence
1st term - (1+1)^2
2nd term - (2+1)^2
3rd term - (3+1)^2
.....so on hence 999th term (999+1)^2 -- SUFFICIENT

All Statement 1 tells you is that the first four terms are 4, 9, 16 and 25. Statement 1 tells you nothing about how the sequence continues beyond the fourth term. The sequence might, for example, be a 'looping' sequence like the following:

4, 9, 16, 25, 4, 9, 16, 25, 4, 9, 16, 25, ...

or of course it could be a sequence of perfect squares:

4, 9, 16, 25, 36, 49, ...

among many possibilities, so Statement 1 is not sufficient.

A sequence is just a list of numbers, in order. The numbers do not *need* to follow any kind of rule or pattern. Don't 'guess' that some rule or pattern exists in a sequence just because a few terms appear to follow some pattern. If you only know the first few terms in a sequence, and you have no rule that lets you predict other terms of the sequence, then the other terms could genuinely be anything at all. In the question above, Statement 1 only tells us the first few terms, so is not sufficient, whereas Statement 2 gives us a rule that lets us predict every term, so is sufficient. The answer is B.