ACT · Intermediate Algebra · Arithmetic and geometric sequences
Question act-q-00367
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The question
An arithmetic sequence has first term 9 and common difference 7. What is the 13th term?
- 93
- 100
- 117
- 31
Show answer & worked solution
Answer: 93
Worked solution. Use aₙ = a₁ + (n − 1)d = 9 + (13 − 1) × 7 = 9 + 84 = 93.
Why each wrong choice is wrong. The (n − 1) factor trips up everyone at first — a distractor uses just n instead, which is consistently off by d.
Test-day tactic. Memorize aₙ = a₁ + (n − 1)d. The (n − 1) is because the first term is at position 1 and has had zero differences added.
About this question type
Arithmetic sequences add a constant; geometric sequences multiply by a constant. Items test the nth-term formulas and occasionally the sum formulas.
You will see a question shaped like this one on roughly every other official ACT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.