Brent@GMATPrepNow wrote: ↑

Sun Aug 28, 2022 9:27 am

What is the value of term_5 of sequence X?

(1) In sequence X, term_1 = 3, term_2 =7, term_3 = 15, and term_4 = 31,
(2) In sequence X, term_6 = 127, term_7 =255, term_8 = 511, and term_9 = 1023

Answer: E
Source: www.gmatprepnow.com

I created this question to highlight the fact that the GMAT does not test our ability to find missing terms in a sequence unless the sequence is defined for us.
The reason is that there's no way that we can definitively determine ONE (and ONLY ONE) pattern in a given sequence.

Consider this example: 1, 2, 4, __
What's the missing term here?
Well, if we read the sequence as doubling from one term to the next, the next term is 8
HOWEVER, if we notice that we keep adding successively larger integers to each term (i.e., add 1, then add 2, then add 3, etc.) the next term is 7

Likewise, (if we want to get a bit silly), we might look at the given sequence (5, 10, 15, 20, 25, __) and say that the next term is 88. Why?
Because 5 is my favorite number, 10 is my 2nd favorite number, 15 is my 3rd favorite number, ... and 88 is 6th favorite number.

Likewise, in this this official GMAT question what-is-the-thousandth-term-of-s-a-cert ... 13904.html, we’re told the first five terms of sequence S are 1², 2², 3², 4², and 5², but that still isn’t enough information to determine the 1000th term.

So, although you might have found a certain pattern in the sequence (double and add 1), we can't be certain that this is THE pattern.
This means t_5 can have ANY numeric value.

Answer: E