Free Practice Quiz Question List

13/14 13. Sequences, Series, and Mathematical Modeling Online Quiz Questions

Use this free practice quiz with 20 questions to review 13/14 13. Sequences, Series, and Mathematical Modeling, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Classify the sequence $7,12,17,22,\ldots$ and identify its constant pattern.

A
Geometric, with common ratio $5$
B
Arithmetic, with common difference $5$
C
Arithmetic, with common difference $12$
D
Geometric, with common ratio $12$

True or false

1 point

True or false: A recursive formula for a sequence must include an initial value in addition to its rule for generating later terms.

A
True
B
False

Written response

1 point

For the geometric sequence $3,12,48,192,\ldots$ , what is the common ratio?

Fill in the blank

1 point

For the arithmetic sequence $7,12,17,22,\ldots$ , the common difference is , and the twentieth term is .

Choose one

1 point

What is the sum of the first 20 terms of the arithmetic sequence $7,12,17,22,\ldots$ ?

A
980
B
1,080
C
1,090
D
1,120

True or false

1 point

True or false: The infinite geometric series with common ratio $r$ converges to a finite sum when $|r|<1$ .

A
True
B
False

Choose all

1 point

Which practices are appropriate when constructing and evaluating a mathematical model? Select all that apply.

A
Identify the quantities and their units
B
Assume that a pattern remains valid indefinitely without checking context
C
Check the model against known values
D
State limitations, especially when extrapolating

Written response

1 point

A town grows by $3\%$ per year. What growth factor should be used in an exponential model for its population?

Choose all

1 point

When choosing among arithmetic, geometric, polynomial, and exponential models, which considerations are relevant? Select all that apply.

A
Whether the input is discrete or continuous
B
Whether outputs have a constant difference or ratio
C
Whether the model automatically remains valid for all possible inputs
D
Whether the domain and real-world limitations are reasonable

Choose one

1 point

The estimated profit is modeled by $P(x)=-0.5x^2+40x-300$ . At how many units sold does the model predict maximum profit?

A
20 units
B
30 units
C
-40 units
D
40 units

Open ended

1 point

Explain how arithmetic and geometric sequences differ, give one example of each, state a formula for each type, and describe when each model is appropriate in a real situation.

Choose one

1 point

Which formula models an account with principal $P$ , annual rate $r$ written as a decimal, $n$ compounding periods per year, and time $t$ in years?

A
$A(t)=P(1+r)^t$
B
$A(t)=P\left(1+\frac{r}{n}\right)^{nt}$
C
$A(t)=P+rt$
D
$A(t)=P\left(1-\frac{r}{n}\right)^{nt}$

Choose one

1 point

An arithmetic sequence has first term $a_1=6$ and common difference $d=4$ . Which explicit formula gives its $n$ th term?

A
$a_n=6+4n$
B
$a_n=6+4(n-1)$
C
$a_n=4(6)^{n-1}$
D
$a_n=6n+4$

True or false

1 point

The infinite geometric series $5+2.5+1.25+\cdots$ converges to a finite sum.

A
True
B
False

Written response

1 point

For the sequence defined by $a_n=3n+2$ , what is the value of $a_{10}$ ?

Written response

1 point

For a quantity modeled as a function of a continuous input, what type of model is appropriate when the output changes by the same percentage for each equal increase in the input?

Choose one

1 point

An account starts with $\$1{,}000$ , earns $6\%$ annual interest, and compounds twice per year. Which model gives its value after $t$ years?

A
$A(t)=1000(1.06)^t$
B
$A(t)=1000(1.06)^{2t}$
C
$A(t)=1000\left(1+\frac{0.06}{2}\right)^{2t}$
D
$A(t)=1000e^{0.06t}$

Choose one

1 point

A quadratic model for profit is $P(x)=-x^2+12x+5$ , where $x$ is the number of units sold. At what value of $x$ does the model predict the maximum profit?

A
$x=0$
B
$x=5$
C
$x=6$
D
$x=12$

Choose one

1 point

The values of a quantity at equally spaced inputs are $1,4,9,16$ . Which model type is suggested by these data?

A
A linear model
B
A quadratic model
C
An exponential model
D
A constant model

Fill in the blank

1 point

A geometric series begins $3+6+12+\cdots$ . What is the sum of its first 6 terms? Enter the value in the blank: