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Quiz #6 Alg 2B sequence/summation - Printable Mathematics Worksheets - Wayground

Quiz #6 Alg 2B sequence/summation

15 questions

11th - 11th Grade

Mathematics

Quiz #6 Alg 2B sequence/summation is a Grade 11 mathematics worksheet that builds fluency with sequence notation, formulas, and summation. Students identify and generate explicit and recursive rules, calculate initial and later terms, determine the number of terms, and recognize common differences in arithmetic sequences and common ratios in geometric sequences. The worksheet also asks students to translate summation notation into an equivalent series and evaluate a sum. The 15-item set includes 14 multiple-choice questions and one fill-in-the-blank item. It gives students practice distinguishing arithmetic from geometric sequences, writing formulas from listed terms or rules, and applying those formulas to find terms such as the 46th or 8th term. Designed for Algebra 2 instruction, independent practice, review, or assessment, this free printable worksheet includes a complete answer key for efficient checking and feedback.

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Quiz #6 Alg 2B sequence/summation

Total questions: 15

Name
Class
Date
1.

Which formula defines the following sequence:

f(1)=2,  f(2)=6,  f(3)=10,  f(4)=14,  f(5)=18f\left(1\right)=2,\ \ f\left(2\right)=6,\ \ f\left(3\right)=10,\ \ f\left(4\right)=14,\ \ f\left(5\right)=18  

a)

f(1)=2,   f(n)=f(n−1)+6 f\left(1\right)=2,\ \ \ f\left(n\right)=f\left(n-1\right)+6\

b)

f(1)=2,  f(n)=f(n−1)+4f\left(1\right)=2,\ \ f\left(n\right)=f\left(n-1\right)+4  

c)

f(1)=2,  f(n)=f(n−1)+2f\left(1\right)=2,\ \ f\left(n\right)=f\left(n-1\right)+2  

d)

f(1)=6,  f(n)=4+f(n−1)f\left(1\right)=6,\ \ f\left(n\right)=4+f\left(n-1\right)  

2.

Given the explicit formula, find the first five terms

a)
b)
c)
d)
3.

Find the explicit formula for the given sequence:

a)

A

b)

B

c)

C

d)

D

4.

Given the explicit formula, find the recursive formula

a)
b)
c)
d)
5.

Find the sum of ∑n=153n − 2  and   ∑n=154n − 1\sum_{n=1}^53n\ -\ 2\ \ and\ \ \ \sum_{n=1}^54n\ -\ 1  

(a)  

6.

This summation is the same as which series?

∑m=16(m − 2)\sum_{m=1}^6\left(m\ -\ 2\right)  

a)
1 + 2 + 3 + 4 + 5 + 6
b)
(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2) + (5 - 2) + (6 - 2)
c)
(1 - 2) + (6 - 2)
d)
(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2)
7.

∑x=39(2x+2)\sum_{x=3}^9\left(2x+2\right)  How many terms are in the sequence?

a)

6

b)

7

c)

3

d)

2

8.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
9.

Create the explicit formula for the sequence: 2, 8, 14, ...

a)
an=2+6n
b)
an=-6+6n
c)
an=6n-4
d)
an=4-6n
10.

Find the 46th term of the arithmetic sequence 3, 8, 13, 18, 23, ...

a)

288

b)

228

c)

338

d)

388

11.

Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

a)

an=6(2)n−1a_n=6\left(2\right)^{n-1}  

b)

an=2(6)n−1a_n=2\left(6\right)^{n-1}  

c)

an=3(2)n−1a_n=3\left(2\right)^{n-1}  

d)

an=2(3)n−1a_n=2\left(3\right)^{n-1}  

12.
Find the first four terms of the sequence given the rule:
an = 4(5)n-1
a)
20, 100, 500, 2500
b)
5, 20, 80, 320
c)
4, 20, 100, 500
d)
4, 9, 14, 19
13.

What is the 8th term in the geometric sequence below?

3, 9, 27, 81, ...

a)

19,683

b)

6,561

c)

2,187

d)

729

14.

Which of the following best describes this sequence?

{135, 45, 15, 5, ...}\left\{135,\ 45,\ 15,\ 5,\ ...\right\}  

a)

An arithmetic sequence with a common ratio of  13\frac{1}{3}  

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of  13\frac{1}{3}  

15.

Which of the following best describes this sequence?

{5, 8, 11, 14, ...}\left\{5,\ 8,\ 11,\ 14,\ ...\right\}  

a)

An arithmetic sequence with a common ratio of 3.

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of 3.

Answer Key

Quiz #6 Alg 2B sequence/summation

Total questions: 15

1.
b)

f(1)=2,  f(n)=f(n−1)+4f\left(1\right)=2,\ \ f\left(n\right)=f\left(n-1\right)+4  

2.
b)
3.
a)

A

4.
c)
5.
90
6.
b) (1 - 2) + (2 - 2) + (3 - 2) + (4 - 2) + (5 - 2) + (6 - 2)
7.
b)

7

8.
c) -11
9.
c) an=6n-4
10.
b)

228

11.
d)

an=2(3)n−1a_n=2\left(3\right)^{n-1}  

12.
c) 4, 20, 100, 500
13.
b)

6,561

14.
d)

A geometric sequence with a common ratio of  13\frac{1}{3}  

15.
c)

An arithmetic sequence with a common difference of 3.

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FAQs

What does this sequences and summation worksheet cover?

This Grade 11 worksheet uses 14 multiple-choice questions and one fill-in-the-blank item to practice explicit and recursive formulas, initial and later terms, term counts, summation-to-series translation, and sums. Students also distinguish arithmetic sequences by common difference from geometric sequences by common ratio, then use those relationships to write rules and find terms such as the 46th or 8th term.

How can I use this worksheet to teach explicit and recursive sequence formulas?

Introduce the worksheet by having students compare a listed sequence with its explicit rule and identify whether the rule gives a term directly or depends on a preceding term. Then model how to generate the first terms, identify a common difference or ratio, and check a formula against the sequence before students complete the multiple-choice items. Use the summation question to connect sigma notation with writing out each term of the corresponding series.

What mistakes should I watch for when students complete this sequence worksheet?

Students may confuse an arithmetic common difference with a geometric common ratio, especially in the classification questions. Watch for indexing errors such as using n instead of n − 1 in a formula, miscounting the number of terms, and selecting a rule that matches later terms but not the first term. When translating summation notation, students may also omit terms or change the expression applied to each term.

How do I assign and grade this sequences and summation worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the 15 items for classwork, homework, or review. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this arithmetic and geometric sequences worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the sequence formulas, summation notation, and answer choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options better support students working with the sequence directions and notation.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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