Free Practice Quiz Question List

10 Sequences and Series Online Quiz Questions

Use this free practice quiz with 20 questions to review 10 Sequences and Series, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

An arithmetic sequence begins $9,13,17,21,\ldots$ . What is $a_{18}$ ?

A
69
B
73
C
77
D
81

True or false

1 point

True or false: A recursive formula for a sequence must include an initial value.

A
True
B
False

Written response

1 point

Find the common ratio of the geometric sequence $81,27,9,\ldots$ .

Fill in the blank

1 point

Complete each statement with the correct term. An ordered list of numbers is a , and the sum of terms from such a list is a .

Choose one

1 point

What is the sixth term of the geometric sequence $5,10,20,40,\ldots$ ?

A
80
B
160
C
320
D
640

Choose all

1 point

Select all correct statements about an infinite geometric series.

A
It has a finite sum when $|r|<1$ .
B
It has a finite sum whenever $|r|>1$ .
C
When it converges, $S_\infty=\frac{a_1}{1-r}$ .
D
Its common ratio must be positive.

True or false

1 point

True or false: A situation with a constant percentage decrease at each step is appropriately modeled by an arithmetic sequence.

A
True
B
False

Written response

1 point

Evaluate $\sum_{k=1}^{5}(2k+1)$ .

Fill in the blank

1 point

Complete the formulas. The sum of the first $n$ terms of an arithmetic sequence is $S_n=$ , and the $n$ th term of a geometric sequence is $a_n=$ .

Choose all

1 point

An arithmetic sequence satisfies $a_4=17$ and $a_{10}=41$ . Select all statements that must be true.

A
The common difference is $4$ .
B
The first term is $5$ .
C
An explicit formula is $a_n=4n+1$ .
D
The 20th term is $76$ .

Open ended

1 point

A student deposits $\$25$ in the first week and increases the deposit by $\$7$ each week. Write an arithmetic formula for the deposit in week $n$ , then find the deposit in week 8 and the total deposited during the first 8 weeks. Show your reasoning.

True or false

1 point

True or false: The sequence $3,-6,12,-24,\ldots$ is geometric with common ratio $-2$ .

A
True
B
False

Choose one

1 point

Which explicit formula represents the sequence $7, 11, 15, 19,\dots$ ?

A
$a_n=4n-1$
B
$a_n=4n+3$
C
$a_n=7n+4$
D
$a_n=3n+4$

Choose one

1 point

What is the common ratio of the geometric sequence $3, 12, 48, 192,\dots$ ?

A
$3$
B
$\frac{1}{4}$
C
$4$
D
$9$

Written response

1 point

The arithmetic sequence begins $7, 11, 15, 19,\dots$ . What is its 25th term?

Choose one

1 point

Evaluate $\displaystyle\sum_{k=1}^{5}(2k+1)$ .

A
$25$
B
$30$
C
$33$
D
$35$

Choose one

1 point

A person deposits $\$40$ in the first week and increases the deposit by $\$5$ each week. What total amount is deposited during the first 12 weeks?

A
$\$810$
B
$\$760$
C
$\$1{,}140$
D
$\$1{,}200$

Choose one

1 point

What is the sum of the first eight terms of the geometric sequence $2, 6, 18, 54,\dots$ ?

A
$3280$
B
$6560$
C
$9840$
D
$13122$

Choose one

1 point

A machine loses 12% of its value each year. Which multiplier should be used to calculate its value after each successive year?

A
0.12, because 12% is written as a decimal
B
0.88, because 100% - 12% = 88% remains
C
1.12, because the decimal is added to 1
D
12.88, because the original amount is combined with the percentage

Written response

1 point

A sequence begins with 18 and each successive term is 4 less than the preceding term. What is the constant additive change from one term to the next?