Question 1

Given the sequence defined by $$a_n = 5n - 4$$, what is the 7th term of the sequence?

Accepted Answer

$$a_7 = 31$

Question 2

Which of the following is the recursive formula for the sequence whose first term is $$a_1 = 1$ and each subsequent term is 5 more than the previous term?

Accepted Answer

$$a_n = a_{n-1} + 5$$

Question 3

Find the first five terms of the sequence defined by $$a_n = 2 \cdot 3$$^{n-1}$$.

Accepted Answer

$$2, 6, 18, 54, 162$$

Question 4

Given the recursive sequence $$a_1 = 2$, a_n = 3a$$_{n-1}$$, what is a_4$?

Accepted Answer

$$54$$

Question 5

Which of the following is the explicit formula for the sequence $$a_1 = 2$, a_n = 3a$$_{n-1}$$?

Accepted Answer

$$a_n = 2 \cdot 3$$^{n-1}$$

Question 6

Evaluate the sum of the first five terms of the sequence $$a_n = \frac{1}{2^n}.$$

Accepted Answer

$$\frac{31}{32}$$

Question 7

A biologist is modeling the population of a bacteria culture using the sequence $$a_n = 2 \cdot 3$$^{n-1}$$. If n$ is the number of hours, what is the population after 6 hours?

Accepted Answer

$$486$$

Question 8

Given the sequence $$a_n = \frac{n}{n+1}$$, what is the limit of $$a_n as$$ $$n 	o \infty$$?

Accepted Answer

$$1$$

Question 9

Which of the following is the correct formula for the $$nth $$term of the sequence $$a_n = \frac{(-1$$)^{n+1}$$(n+1)}{3^n}$$?

Accepted Answer

$$a_n = \frac{(-1$$)^{n+1}$$(n+1)}{3^n}$$

Question 10

The Fibonacci sequence is defined by $$f_1 = 1$, f_2$ = 1$$, $$f_n = f_{n-1} + f_{n-2}. $$What is $$f_6$$?

Accepted Answer

$$8$$

Question 11

A chemist is studying a reaction where the concentration of a substance follows the sequence $$a_n = 5n - 4. $$What is the difference in concentration between the 10th and 5th measurements?

Accepted Answer

$$25$$

Question 12

Given the sequence $$a_n = \frac{2}{5}, \frac{3}{25}, \frac{4}{125}, \frac{5}{625}, \frac{6}{3125}, \ldots$$, what is the general formula for $$a_n$$?

Accepted Answer

$$a_n = \frac{n+1}{5^n}$$

Question 13

Which of the following sequences is neither arithmetic nor geometric?

Accepted Answer

$$a_n = \frac{n}{n+1}$$

Question 14

A medical researcher is tracking the number of patients in a study using the recursive formula $$a_1 = 1$, a_n = a$$_{n-1} + 5$$. How many patients are there after 8 intervals?

Accepted Answer

$$36$$

Question 15

If $$a_n = \frac{1}{2^n}$$, which of the following best describes the behavior of the sequence as $$n$$ increases?

Accepted Answer

The terms approach $$0 as$$ $$n$$ increases.

Question 16

Which of the following is the correct recursive formula for the Fibonacci sequence?

Accepted Answer

$$f_1 = 1$$,\ $$f_2 = 1$$,\ f_n = f_{n-1} + f_{n-2}$$

Question 17

A sequence is defined by $$a_1 = 1$, a_n = a$$_{n-1} + 5$$. What is the explicit formula for a_n$?

Accepted Answer

$$a_n = 5n - 4$$

Question 18

Which of the following best describes the sequence $$a_n = (-1$$)^{n+1}$$(n+1)/3^n$$?

Accepted Answer

An alternating sequence whose terms decrease in magnitude as $$n$$ increases.

Question 19

A sequence is defined by $$a_n = \frac{n}{n+1}. $$What is $$a_5$$?

Accepted Answer

$$\frac{5}{6}$$

Introduction to Sequences: Definitions, Formulas, and Examples

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