Quick Answer
A sequence is an ordered list of numbers following a specific rule. On the Digital SAT, sequences appear in the Math section, typically within Advanced Math. These questions occur approximately once or twice per test, requiring students to identify patterns or calculate specific terms using arithmetic or geometric formulas.
A sequence is a mathematical function whose domain is a set of consecutive integers, representing an ordered list of terms. Each term is denoted as $a_n$, where $n$ is the position of the term in the list.
Question: In an arithmetic sequence, the first term is 12 and the common difference is 5. What is the value of the 15th term? Solution: Use the arithmetic sequence formula $a_n = a_1 + (n - 1)d$. Here, $a_1 = 12$, $d = 5$, and $n = 15$. Calculation: $a_{15} = 12 + (15 - 1)5 = 12 + (14 \times 5) = 12 + 70 = 82$.
Off-by-one errors: Students often forget to use $(n-1)$ in the formula, incorrectly multiplying the difference by the full term number.
Confusing arithmetic and geometric rules: Applying a common difference (addition) to a problem that requires a common ratio (multiplication).
Misidentifying the starting term: Using the value of the second term as $a_1$ when the problem provides a list or a table.
Students targeting 750+ should know that sequences are discrete versions of linear and exponential functions. An arithmetic sequence is essentially a linear function with a slope equal to the common difference, while a geometric sequence is an exponential function. You can use the Desmos calculator to plot these terms as points and find the regression equation if you forget the specific sequence formulas.
Arithmetic Sequence
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. On the Digital SAT, this concept appears in the Math section, typically within Module 2 as a more advanced linear relationship question. It tests a student's ability to identify patterns and apply the nth term formula to find specific values.
Function
A function is a mathematical relationship where each input maps to exactly one output. On the Digital SAT, functions are tested heavily in the Math section, appearing in approximately 25% of Algebra and Advanced Math questions. Students must evaluate equations or interpret graphs to identify specific output values.
Geometric Sequence
A geometric sequence is a numerical list where each term is found by multiplying the previous term by a constant ratio. On the Digital SAT, these concepts typically appear in the Math section (Module 1 or 2) approximately once per test, usually within word problems involving exponential growth or decay.
Variable
A variable is a symbol, usually a letter, representing an unknown or changing numerical value. On the Digital SAT, variables are foundational to the Math section, appearing in approximately 70% of questions. They are most prevalent in algebra problems where students must solve for a specific unknown or model real-world relationships.
A sequence on the SAT is an ordered list of numbers that follows a consistent mathematical rule. These typically appear in the Math section as arithmetic or geometric patterns. Students must identify the logic behind the numbers to find missing terms or predict future values. They are essential for understanding growth models in advanced math problems.
To calculate a term in a sequence, first determine if the pattern is arithmetic (adding/subtracting) or geometric (multiplying/dividing). For arithmetic sequences, use the formula $a_n = a_1 + (n-1)d$. For geometric sequences, use $a_n = a_1 \times r^{(n-1)}$. Identifying the first term and the constant rate of change is necessary for solving these questions on the SAT.
A sequence is a list of individual numbers in a specific order, while a series is the sum of those numbers. The Digital SAT focuses almost exclusively on sequences, asking students to find specific terms or rules. You are rarely required to calculate the sum of a series, but understanding that a sequence is the underlying list is fundamental.
Typically, you will encounter approximately one to two questions regarding sequences on the Digital SAT Math section. These questions are often found in the 'Advanced Math' category. While they are not the most frequent topic, they often appear as medium-to-hard difficulty questions in the second module, making them important for students aiming for high scores.
