GMAT Test Tip - Sequences

Sequence problems can look daunting at first, but there are really just two main types. If you know the basic strategy for each main type, you’ll have the first step finished when you see them on the GMAT.

All sequence questions will present you with some formula that defines the sequence. The two types are recognized by how they ask the question:

Type 1: First 5 – 10 Terms
Question example: What is the 7th term in the sequence?

Strategy: Solve the sequence. It may seem like a lot of work, but it’s the only right thing to do.

Example:
The first term of the sequence is 4, and thereafter, every term is defined by:

See Image #1

What is the 6th term in the sequence?

To solve this, though it seems tedious, just list out the terms until you hit the 6th one:

1st term: 4
2nd term: 5
3rd term: 7
4th term: 11
5th term: 19
6th term: 35

Answer: 35

Type 2: Very Far Away Terms
Question sample: What is the sum of the first 1,000 terms?

Strategy: Solve out the first few terms of the sequence until a pattern emerges. There will always be a pattern (they don’t really want you to add up all 1,000 terms), and once you find it, you’ll have the answer.

Example:
In a certain sequence, the first term is –2, and the second term is 2. If every term thereafter is defined by:

See Image #2

What is the sum of the first 700 terms?

To solve this, recognize that you won’t have to list out all 700 terms. Just list them out until the pattern emerges:

1st term: -2
2nd term: 2
3rd term: 4
4th term: 2
5th term: -2
6th term: -4
7th term: -2
8th term: 2
9th term: 4

What you should see is that this sequence repeats itself every 6 terms. That is the pattern. So you only have to figure out the sum of the first 6 terms and then figure out how many times the pattern repeats itself over 700 terms.

But the GMAT doesn’t usually ask so much from us. Notice that the sum of the first 6 terms is zero! That means every six, the whole sequence is zero. All that’s left to do is figure out what’s left over at the end of the sequence.

700 divided by 6 is 116, with a remainder of 4. So at the 700th term we are on the 4th term of our repeating set: -2, 2, 4, 2, the sum of which is 6.

To Recap:
If the question asks about the first 5 – 10 terms, do the math. If it asks about a very far away term, look for the pattern.