## What is the thousandth term of S, a certain sequence of numbers? (1) For every n, the nth term of S is n^2.

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### What is the thousandth term of S, a certain sequence of numbers? (1) For every n, the nth term of S is n^2.

by BTGmoderatorDC » Mon Mar 20, 2023 2:11 pm

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What is the thousandth term of S, a certain sequence of numbers?

(1) For every n, the nth term of S is n^2.
(2) The first five terms of S are 1^2, 2^2, 3^2, 4^2, and 5^2.

OA A

Source: GMAT Prep

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### Re: What is the thousandth term of S, a certain sequence of numbers? (1) For every n, the nth term of S is n^2.

by [email protected] » Fri Mar 24, 2023 6:09 am

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BTGmoderatorDC wrote:
Mon Mar 20, 2023 2:11 pm
What is the thousandth term of S, a certain sequence of numbers?

(1) For every n, the nth term of S is n^2.
(2) The first five terms of S are 1^2, 2^2, 3^2, 4^2, and 5^2.

OA A

Source: GMAT Prep
Target question: What is the value of term_1000?

Statement 1: For every n, the nth term of S is n².
Perfect! Statement 1 provides a "recipe" for determining the value of ANY term in the sequence.
So, it must be the case that term_1000 = 1000² = 1,000,000
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The first five terms of S are 1², 2², 3², 4², and 5².
Important: Even though it certainly LOOKS like there is a pattern here, we can't assume that it continues,
For example, the sequence COULD just be a list of someone's favorite numbers.
So, it COULD be the case that term_6 = 17², term_7 = 5.3, term_8 = -9.22, etc, in which case, term_1000 can have pretty much any value
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT