ACT · Intermediate Algebra · Arithmetic and geometric sequences
Question act-q-00375
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The question
An arithmetic sequence has first term 4 and common difference 4. What is the 9th term?
- 100
- 40
- 163
- 36
Show answer & worked solution
Answer: 36
Worked solution. Use aₙ = a₁ + (n − 1)d = 4 + (9 − 1) × 4 = 4 + 32 = 36.
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.