ACT · Intermediate Algebra · Arithmetic and geometric sequences
Question act-q-00370
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The question
An arithmetic sequence has first term 3 and common difference 2. What is the 19th term?
- 41
- 39
- 57
- 55
Show answer & worked solution
Answer: 39
Worked solution. Use aₙ = a₁ + (n − 1)d = 3 + (19 − 1) × 2 = 3 + 36 = 39.
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 the back end of the section, where the score gradient is steepest. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.