Quick Answer
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.
An arithmetic sequence is a numerical progression where each subsequent term is found by adding a fixed constant, known as the common difference (d), to the preceding term. The general formula for the nth term is a_n = a_1 + (n - 1)d, where a_1 is the first term.
Question: In an arithmetic sequence, the 3rd term is 12 and the common difference is 5. What is the 10th term? Solution: Use the formula a_n = a_3 + (n - 3)d. Here, a_10 = 12 + (10 - 3)5. Calculation: 12 + (7)(5) = 12 + 35 = 47. Alternatively, find a_1: 12 = a_1 + (3-1)5, so a_1 = 2. Then a_10 = 2 + (9)(5) = 47.
Off-by-one error: Students often use 'n' instead of '(n-1)' in the formula, forgetting that the common difference is added only after the first term.
Confusing with Geometric: Students may multiply by the common difference instead of adding it, confusing linear growth with exponential growth.
Misidentifying the difference: Calculating the difference as (a_n - a_n+1) instead of (a_n+1 - a_n), leading to an incorrect sign for the common difference.
Students targeting 750+ should know that an arithmetic sequence is simply a linear function f(n) = dn + (a_1 - d) where the domain is restricted to integers. Recognizing the common difference as the 'slope' allows you to use the linear equation y = mx + b and the Desmos calculator to solve sequence problems rapidly by looking for points on a line.
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.
Sequence
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.
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