What Is Sequences on the GMAT?
Sequences on the GMAT are ordered lists of numbers that follow a specific pattern. They appear frequently in the Quantitative section, testing your ability to recognize patterns, apply formulas, and solve problems efficiently.
Definition
A sequence is a list of numbers arranged in a specific order, often following a rule or pattern. Each number in the sequence is called a term, and its position is denoted by a subscript (e.g., a1 is the first term, an is the n-th term).
Common types include arithmetic sequences (constant difference between terms) and geometric sequences (constant ratio between terms), but GMAT sequences can be defined by any rule, such as recursive formulas or patterns involving squares, cubes, or alternating signs.
Why It Matters on the GMAT
Sequence problems test your ability to identify patterns and apply algebraic reasoning. They often appear in both Problem Solving and Data Sufficiency questions. You may be asked to find a specific term, the sum of terms, or to determine a rule based on given terms.
Mastering sequences helps you tackle a range of algebra and number property questions, and it sharpens your logical thinking for other GMAT problems.
A Concrete Example
Consider the sequence: 2, 5, 8, 11, ...
This is an arithmetic sequence with a common difference of 3. The n-th term can be found using the formula:
an = a1 + (n-1)d
So, the 10th term is a10 = 2 + (10-1)*3 = 2 + 27 = 29.
If the question asks for the sum of the first 10 terms, you can use the formula:
Sn = n/2 * (a1 + an)
Thus, S10 = 10/2 * (2 + 29) = 5 * 31 = 155.
Common Mistakes
- Assuming a sequence is arithmetic or geometric without checking: Always verify the pattern using multiple terms.
- Misidentifying the term number: For example, confusing the 5th term with n=5 when the sequence starts at n=1.
- Ignoring the possibility of multiple patterns: Some sequences can be defined in more than one way; look for the simplest rule that fits all given terms.
- Forgetting to apply the correct formula: For sum of an arithmetic sequence, use the average of first and last term times the number of terms; for geometric, use the specific sum formula.
How to Practice It
Start by identifying the type of sequence from a few terms. Practice writing recursive formulas (e.g., an = an-1 + d) and explicit formulas (an = a1 + (n-1)d).
Work on GMAT-style problems from official guides or reputable online sources. Time yourself to improve speed. Also, practice Data Sufficiency questions involving sequences, as they require careful analysis of what information is sufficient.
For more detailed strategies and practice questions, visit our Sequences page.