What is the 999th term of the series S ? (1) The first four terms of S

I understand where you are coming from. We have done those sort of questions. Given a series 1^2, 2^2, 3^2, 4^2.. then automatically the next thing which comes to mind is 5^2. It seems that there cannot be anything else, because from the first four terms, it seems that the pattern for each term is n^2.

But since this is a GMAT data sufficiency question, we cannot assume that would be the case. Its possible that i decide to make a series where the first four terms follow the rule n^2, next four terms follow (n+1)^2, next four terms follow (n+2)^2 and so on.. In that case the series will look like this:
1, 4, 9, 16, 36, 49, 64, 81, 121, 144,...

So how do we know that the given series (as per first statement) is not something like this. How do we know that ALL terms will follow n^2 or (n+1)^2?
That is what is specified only in second statement.

I understand where you are coming from. We have done those sort of questions. Given a series 1^2, 2^2, 3^2, 4^2.. then automatically the next thing which comes to mind is 5^2. It seems that there cannot be anything else, because from the first four terms, it seems that the pattern for each term is n^2.

But since this is a GMAT data sufficiency question, we cannot assume that would be the case. Its possible that i decide to make a series where the first four terms follow the rule n^2, next four terms follow (n+1)^2, next four terms follow (n+2)^2 and so on.. In that case the series will look like this:
1, 4, 9, 16, 36, 49, 64, 81, 121, 144,...

So how do we know that the given series (as per first statement) is not something like this. How do we know that ALL terms will follow n^2 or (n+1)^2?
That is what is specified only in second statement.[/quote]


Thanks, Aman.

Indeed, it's one of those lessons learned in school to assume based on the first few terms.
Will keep this in mind, thanks again

Statement 1: we know the first \(4\) terms but what about terms after that? They could be anything. Hence insufficient

Statement 2: This clearly mentions the value of each term in the series.

So 999th term will be \((999+1)^2=1000^2\). Sufficient

Option B

Can someone explain why A as well cannot provide an answer?
The first four terms of the series are given and we are asked to find the 999th term. If we see a pattern in a series(and we know at least two terms), can we not find the nth term?

Or did I not get the question correctly?