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How to solve question #12 on page 168 in The Official Guide to the GRE, 3rd ed.

I assign most of the problems in The Official Guide to the GRE, 3rd ed. as homework for my comprehensive online GRE prep courses. While the book does provide answer explanations for many of them, they aren’t always clear and often take a more traditional mathematical approach than what is necessary (they don’t employ the non-standard math strategies I teach, for example).

For whatever reason, students seem to have particular difficulty with the following GRE sequence question:

The sequence of numbers a₁, a₂, a₃, …, a?, … is defined by a? = 1/n – 1/(n+2) for each integer n ≥ 1. What is the sum of the first 20 terms of the sequence?

(A) (1 + ½) – 1/20
(B) (1 + ½) – (1/21 + 1/22)
(C) 1 – (1/20 + 1/22)
(D) 1 – 1/22
(E) 1/20 – 1/22

This is question #12 on page 168 in The Official Guide to the GRE and I get questions about it all the time. As such, I took the liberty of recording a short video (see above) where I explain how to solve this question in detail.

First, I teach some basics about mathematical sequences that will help you dominate any sequence question the GRE might throw at you. Think of it as another building block for you to work with (see: The LEGO Approach to Optimal Test Preparation)!

Then, I apply that understanding to this particular question. I think it’ll clear up a lot of confusion for you and put you in a stronger position to get more right answers on test day.

What did you find helpful? What are you still confused about? Post your comments/questions below. I’m here to help!