Arithmetic Sequences on the SAT
Arithmetic sequences appear when a quantity changes by the same amount each step. SAT questions may give several terms and ask for a later term. They may also provide two distant terms and require the common difference. The key is identifying what stays constant. In an arithmetic sequence, consecutive terms have one fixed difference.
Using the Explicit Formula
The explicit formula connects any term directly to the first term. Start with the first term, then add the common difference repeatedly. The factor n minus one counts how many jumps occur before reaching the nth term. This method is efficient when the SAT asks for a distant term. It also avoids listing every value in a long sequence.
Finding Missing Information
Sometimes the first term is unknown. A known term and the common difference can recover it. Other problems give two known terms. Subtract their values, then divide by the difference between their term numbers. This produces the common difference. If a target value is provided, rearrange the explicit formula to solve for its term index.
Arithmetic Series and SAT Word Problems
An arithmetic series is the sum of arithmetic sequence terms. SAT problems can describe repeated deposits, seating rows, increasing distances, or other steady changes. Translate the situation into a first term, a common difference, and a term count. Then choose either the nth-term formula or the sum formula. Always check whether the question asks for one term or a total.
Checking Your Work
After solving, substitute the result back into the sequence rule. A valid term index should usually be a positive integer. Generated terms should change by the same difference each time. This calculator shows formulas, substitutions, and generated values so you can inspect the logic before accepting an answer. Practicing several forms makes SAT sequence questions much easier to recognize.