Key Information to Know About Sequences

Hey guys! When we see sequences on the GMAT whether in the problem solving or the data sufficiency section they have two important characteristics. One is how they work, the other is anchoring the sequence to a particular set of numbers. Let’s start by taking a look at the most basic sequence out there. Counting! The way counting works is that every time we go up a term in the sequence we add one and if we take number one as our first term then the term number and the value move in tandem. First term is 1. Second term is 2, 50th term is 50. We could also anchor it differently. Let’s say we wanted to say the first term is five, then the second term is six, third term is seven, fourth term is eight, so on and so forth.

Play around with this: do it with the even numbers or the odd numbers and try different anchor points. Sequences can seem more complicated than they are because we don’t think of them in this basic sort of way and because they’re expressed oftentimes with weird notation. So when we see some sequence with a little number below, it that’s called a Subscript. That tells you the number of term of the sequence that they’re talking about. So going back to our counting example, S1 the first term in the sequence equals 1. S2 equals 2, S sub 3 equals 3. If we were doing the even numbers starting at two S sub 1 equals 2, S sub 2 equals 4, S sub 3 equals 6, S sub 10 equals 20. So don’t get freaked out by the notation just because it looks like it comes out of some very crazy math book.

What We Need

The problem we’re going to look at today is asking us for the value of a specific term within a sequence and the what do we need comes in two parts. We need both how the sequence works and we need to know (not necessarily where it starts) but some anchor point to tell us what some term is relative to the sequence so we can figure out any other term above or below that. We’re going to say that again: we don’t need the beginning or ending term, just any term with a specific value that along with the rules allows us to get to any other place in the sequence.

Which Statement to Begin With

Generally, when we are looking for two pieces of information we should be attuned to looking for a (C) or an (E) answer choice but that’s not always the case. If we dive into the introduced information, we’ll start with number 2 and the reason is that it’s going to be easier to evaluate. At first glance it’s simpler and you always want to start out with the easier piece and work your way up. Number 2 gives us a term. It gives us the first term, but we don’t know how the sequence works therefore it’s insufficient. Number 1 gives us the 298th term and describes how the sequence works so we’re getting both pieces together in number 1.


Therefore (A) 1 alone is sufficient. Notice here that because we’re primed for (C) / (E) answer choice, looking for two pieces of information, the GMAT is betting that we think to ourselves hey I need the first term in this sequence and the 298th term doesn’t tell me anything. They’re looking for us to answer (C) that we need them both. But once you understand sequences you’ll never fall for it. Hope this helped guys, check out other sequence problems below and we’ll see you again soon.

If you enjoyed this GMAT sequences video, try your hand at this Ratio problem next.