AP PreCalculus Practice Quiz: Change in Arithmetic and Geometric Sequences
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) A common ratio
B) A common difference
C) A variable rate of change
D) A proportional difference
Correct Answer: B
Based on the provided content, "Successive terms in an arithmetic sequence have a common difference, or constant rate of change."
A) An arithmetic sequence
B) A geometric sequence
C) A Fibonacci sequence
D) A harmonic sequence
Correct Answer: B
The content states, "Successive terms in a geometric sequence have a common ratio, or constant proportional change."
A) aₙ = a₀ * dⁿ
B) aₙ = a₀ + n/d
C) aₙ = a₀ + dn
D) aₙ = d + a₀ⁿ
Correct Answer: C
The provided content specifies that "The general term of an arithmetic sequence with a common difference d is denoted by aₙ and is given by aₙ = a₀ + dn, where a₀ is the initial value."
A) gₙ = g₀ + rn
B) gₙ = g₀ * rⁿ
C) gₙ = g₀ * nʳ
D) gₙ = r + g₀ * n
Correct Answer: B
According to the content, "The general term of a geometric sequence with a common ratio r is denoted by gₙ and is given by gₙ = g₀rⁿ, where g₀ is the initial value."
A) A continuous curve connecting all points
B) A series of vertical bars
C) A set of discrete points
D) A smooth, unbroken line
Correct Answer: C
The content states, "the graph of a sequence consists of discrete points instead of a curve." This is because a sequence is a function from the whole numbers, not all real numbers.
A) aₙ = 5 + 3n
B) aₙ = 3 + 5n
C) aₙ = 5 * 3ⁿ
D) aₙ = 3 * 5ⁿ
Correct Answer: A
The initial value a₀ is 5. The common difference d is 8 - 5 = 3. Using the formula aₙ = a₀ + dn, the function is aₙ = 5 + 3n.
A) gₙ = 2 + 3n
B) gₙ = 3 + 2n
C) gₙ = 2 * 3ⁿ
D) gₙ = 3 * 2ⁿ
Correct Answer: C
The initial value g₀ is 2. The common ratio r is 6 / 2 = 3. Using the formula gₙ = g₀rⁿ, the function is gₙ = 2 * 3ⁿ.
A) aₙ = 15 + 50n
B) aₙ = 50 * 15ⁿ
C) aₙ = 50 + 15n
D) aₙ = 15 * 50ⁿ
Correct Answer: C
This scenario describes an arithmetic sequence. The initial value a₀ is $50. The common difference d (the constant amount added each week) is $15. The general term is given by aₙ = a₀ + dn, which is aₙ = 50 + 15n.
A) gₙ = 100 + 2n
B) gₙ = 2 * 100ⁿ
C) gₙ = 2 + 100n
D) gₙ = 100 * 2ⁿ
Correct Answer: D
This scenario describes a geometric sequence because the population changes by a constant proportion (doubling). The initial value g₀ is 100. The common ratio r is 2. The general term is given by gₙ = g₀rⁿ, which is gₙ = 100 * 2ⁿ.
A) A geometric sequence with an initial value of 20 and a common ratio of -4.
B) An arithmetic sequence with an initial value of 20 and a common difference of -4.
C) A geometric sequence with an initial value of 16 and a common ratio of -4.
D) An arithmetic sequence with an initial value of -4 and a common difference of 20.
Correct Answer: B
The function is in the form aₙ = a₀ + dn. Comparing f(n) = 20 - 4n to the general form, the initial value a₀ is 20 and the common difference d is -4. This represents an arithmetic sequence.
A) It is a geometric sequence with a ratio greater than 1.
B) It is a geometric sequence with a ratio between 0 and 1.
C) It is an arithmetic sequence.
D) It is neither arithmetic nor geometric.
Correct Answer: C
An arithmetic sequence has a constant rate of change (common difference), which corresponds to the slope of a line. Since the graph of a sequence consists of discrete points, points lying on a straight line indicate an arithmetic sequence.
A) The real numbers
B) The rational numbers
C) The integers
D) The whole numbers
Correct Answer: D
The provided content explicitly states, "A sequence is a function from the whole numbers to the real numbers." Therefore, the domain is the set of whole numbers.
A) gₙ = 25000 - 0.15n
B) gₙ = 25000(0.15)ⁿ
C) gₙ = 25000(0.85)ⁿ
D) gₙ = 25000(1.15)ⁿ
Correct Answer: C
This is a geometric sequence because the value changes by a constant proportion each year. The initial value g₀ is 25,000. If the value depreciates by 15%, it retains 100% - 15% = 85% of its value. Therefore, the common ratio r is 0.85. The function is gₙ = g₀rⁿ, or gₙ = 25000(0.85)ⁿ.
A) Arithmetic sequences change by a constant amount, while geometric sequences change by a variable amount.
B) Arithmetic sequences have a constant rate of change, while geometric sequences have a constant proportional change.
C) Both sequences have a constant rate of change, but it is additive for arithmetic and multiplicative for geometric.
D) Arithmetic sequences model linear growth, while geometric sequences model quadratic growth.
Correct Answer: B
The content states that successive terms in an arithmetic sequence have a "common difference, or constant rate of change", while successive terms in a geometric sequence have a "common ratio, or constant proportional change". This option directly reflects that distinction.
A) aₙ = 12 - 3n
B) aₙ = 12 + 3n
C) aₙ = 12 * (3/4)ⁿ
D) aₙ = 9 + 3n
Correct Answer: A
The initial value a₀ is 12. The common difference d is the difference between successive terms, which is 9 - 12 = -3. Using the formula aₙ = a₀ + dn, the function is aₙ = 12 + (-3)n, or aₙ = 12 - 3n.
A) It is an arithmetic sequence because the change is constant.
B) It is a geometric sequence because it follows the form gₙ = g₀rⁿ.
C) It cannot be a sequence because its graph is a curve.
D) It is an arithmetic sequence because b represents the common difference.
Correct Answer: B
The function gₙ = g₀rⁿ for a geometric sequence is an exponential function where the domain is restricted to whole numbers. The graph of such a function would be discrete points that lie on an exponential curve. Therefore, the sequence is geometric. Option C is incorrect because the graph consists of discrete points, not a continuous curve.