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AP Precalculus

AP Precalc 2.1–2.3: Mixed Practice MCQ (Set D)

Shared by ashtont · Oct 26, 2026 · 0 plays

16 new hard questions mixing all of 2.1–2.3: sequence formulas from two terms, factors over 2- and 3-unit intervals, decay reflected, range after a shift, percent growth and rates of change. Different questions from Sets A–C. Every choice has an explanation.

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16 questions across 4 sections. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Sections (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

An arithmetic sequence has a₆ = 22 and a₁₁ = 7. What is a₁?
  1. A. 37 ✓
  2. B. 40
  3. C. 7
  4. D. 52

Correct answer: A. D = (7 − 22)/(11 − 6) = −15/5 = −3. Going back 5 steps from a₆: a₁ = 22 − 5(−3) = 37.

A geometric sequence has g₂ = 18 and g₅ = −2/3. What is g₇?
  1. A. 2/27
  2. B. 2/9
  3. C. −2/27 ✓
  4. D. 2/81

Correct answer: C. R³ = (−2/3)/18 = −1/27, so r = −⅓. Then g₇ = g₅ · r² = (−2/3)(1/9) = −2/27.

The sequence aₙ = 5 − 2n (n = 1, 2, 3, …) and the function f(x) = 5 − 2x have the same rule. Which of the following is true?
  1. A. The common difference of aₙ is −2, the slope of f, and the graph of aₙ is separate points that lie on the line y = 5 − 2x. ✓
  2. B. The common difference of aₙ is 5, because 5 is the starting value of the rule.
  3. C. The common difference of aₙ is 3, because a₁ = 3.
  4. D. aₙ is geometric, because its terms decrease.

Correct answer: A. Each step in n changes the term by −2, the same as the slope of f. The sequence only has whole-number inputs, so its graph is points on f's line, not the whole line.

Which of the following could NOT be the first four terms of a geometric sequence?
  1. A. ¼, ½, 1, 2
  2. B. 5, −5, 5, −5
  3. C. 0.2, 0.02, 0.002, 0.0002
  4. D. 3, 6, 12, 18 ✓

Correct answer: D. 6/3 = 2 and 12/6 = 2, but 18/12 = 1.5. The ratio isn't constant, so it isn't geometric. (It isn't arithmetic either: differences 3, 6, 6.)

x: −2, 0, 2, 4 | f(x): 75, 15, 3, 0.6 — The function f is exponential. Selected values are shown in the table. What is f(6)?
  1. A. 0
  2. B. 0.12 ✓
  3. C. −1.8
  4. D. 0.024

Correct answer: B. Every 2-unit step multiplies the output by 15/75 = 3/15 = 0.6/3 = ⅕. So f(6) = 0.6 · ⅕ = 0.12.