Question 1

Which of the following best describes an arithmetic sequence?

Accepted Answer

A sequence where each term is found by adding a constant value to the previous term.

Question 2

Given the arithmetic sequence $$5, 9, 13, 17, \ldots$$, what is the common difference?

Accepted Answer

$$4$$

Question 3

Which of the following is a geometric sequence?

Accepted Answer

$$2, 4, 8, 16, 32$$

Question 4

If a geometric sequence has a first term of $$100$$ and a common ratio of $$0.5$$, what is the fourth term?

Accepted Answer

$$12.5$$

Question 5

A sequence is defined recursively by $$a_1 = 3$ and a$$_{n+1} = a_n + 7$$. What is a_4$?

Accepted Answer

$$17$$

Question 6

Which of the following is the correct recursive definition for the geometric sequence $$a_1 = 6$, a_2$ = 12$$, $$a_3 = 24$, a_4$ = 48$$, ...?

Accepted Answer

$$a_1 = 6$, a$$_{n+1} = 2a_n$$

Question 7

A real-world scenario: A population of bacteria triples every hour. If there are $$200$$ bacteria at the start, how many will there be after $$4$$ hours?

Accepted Answer

$$16,200$$

Question 8

Given the arithmetic sequence $$a_n = 15 - 4n$$, what is the common difference?

Accepted Answer

$$-4$$

Question 9

Which function notation correctly represents the $$nth $$term of the geometric sequence $$a_1 = 2$, r = 5$?

Accepted Answer

$$a_n = 2 \cdot 5$$^{n-1}$$

Question 10

A sequence is defined by $$a_1 = 10$ and a$$_{n+1} = 0.8a_n$$. What type of sequence is this, and what is the common ratio?

Accepted Answer

Geometric, common ratio $$0.8$$

Question 11

If the arithmetic sequence $$a_1 = 7$ and a_5$ = 31$$, what is the common difference?

Accepted Answer

$$6$$

Question 12

A car’s value depreciates by $$20\%$$ each year. If the car is worth $$\25$$,000$$ now, what will it be worth after 3$ years? (Round to the nearest dollar.)

Accepted Answer

$$\12$$,800$

Question 13

Which of the following is NOT a way to represent a sequence?

Accepted Answer

As a single number

Question 14

Given the sequence $$a_n = 3 \cdot 2$$^{n-1}$$, what is a_5$?

Accepted Answer

$$48$$

Question 15

A savings account earns $$5\%$$ interest compounded annually. If you deposit $$\1$$,000$$, how much will you have after 3$ years? (Round to the nearest dollar.)

Accepted Answer

$$\1$$,157$

Question 16

Which recursive formula defines the arithmetic sequence $$12, 9, 6, 3, \ldots$$?

Accepted Answer

$$a_1 = 12$, a$$_{n+1} = a_n - 3$$

Question 17

If a sequence is defined by $$a_n = 7n - 2$$, what is the $$10th $$term?

Accepted Answer

$$68$$

Question 18

A medication’s concentration in the bloodstream halves every $$6$$ hours. If the initial concentration is $$80 mg/L$$, what will it be after $$18$$ hours?

Accepted Answer

$$10 mg/L$$

Question 19

Which of the following best describes the domain of a sequence?

Accepted Answer

All positive integers

Question 20

A sequence is defined by $$a_1 = 2$ and a$$_{n+1} = 3a_n + 1$$. What is a_3$?

Accepted Answer

$$20$$

Sequences: Types, Properties, and Representations

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