GMAT Tip: Making the Abstract Concrete

The secret is that sequence problems are much more structured than they first appear Photograph by Getty Images

This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.

Generally speaking, GMAT students approach sequence problems by employing this sequence: (1) Notice abstract notation in sequence problem; (2) sigh frustratedly; (3) rub palm against temples and stare at problem; and (4) guess and move on.

Obviously, that’s not the best way to approach sequence problems, which are almost always more manageable than they first appear. What makes sequence problems so difficult? Typically, it’s the abstract, cumbersome notation. For example, what does this even mean?

For all values n > 2, an = an-2 – an-1. If a1 = 4 and a2 = 2…

Here’s the secret: This is much more structured than it looks. The subscript “n” in all of these questions just signifies the number of the term in the sequence. So your strategy should always be to: (1) Write down the first few terms to get a feel for how the structure looks; and (2) try to interpret the way that future terms are calculated.

Here, you have the first two terms already:

First Term: 4

Second Term: 2

And if you interpret the relationship for the rest, it’s basically telling you “to get the third term in the sequence, take the first one, and subtract the second one.” It’s just doing so in awful language. If you plug in n = 3, this is what you get:

an-2 – an-1

a1 – a2

4 – 2

Third term: 2

To get the rest of the terms in the sequence,  just follow the rule: “To get the next term, take the one from two ago and subtract the previous one.” So the fourth term will be 2 – 2 = 0, the fifth term will be 2 – 0 = 2, and so on.

You can fill in as many terms for the rest of the sequence as you want, and in almost every GMAT sequence problem it will either be something you can solve within the first handful of terms or a sequence that forms a pattern you can extrapolate to solve the questions. In almost every GMAT sequence problem, the hardest part is knowing where to begin. So remember: The subscripted variable just tells you which term it is in the sequence. From there, your sequence of events on sequence problems should be:

(1) Write out the known terms;

(2) Interpret the way that future terms are calculated;

(3) Either solve the problem based on that interpretation, if you can, or continue writing out terms until you’ve solved the problem in a few terms or found the pattern.

Brian Galvin has studied the GMAT full time since 2006 as the director of academic programs for Veritas Prep. He received a Masters in Education from the University of Michigan and is the proud owner of a 99th percentile GMAT score.

For more GMAT advice from Veritas Prep watch “GMAT Tip: Simple Solution to Sequence Problems”

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