Algebra 2 Sequences Series Quiz – Free PDF

Contents

This algebra 2 sequences series quiz asks 10 multiple-choice questions on sequences and series, and each answer comes with a short explanation.

Ten multiple-choice questions check explicit and recursive formulas, sigma notation, series sums and money applications. Pick the single best answer; the explanation after each question shows the common mistake.

Algebra 2Common Core: A-SSE.B.4 · F-BF.A.2 · F-IF.A.3

🎯 Sequences and Series – Algebra 2 math quiz

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Question 1

What is the common difference of the sequence graphed below?

Points $(n,a_{n})$.

A $-6$

B $6$

C $-5$

D $-12$

Question 2

If $a_{n}=3\cdot 2^{n-1}$, what is $a_{6}$?

A $192$

B $36$

C $48$

D $96$

Question 3

Which recursive formula generates $5,\,15,\,45,\,135$?

A $a_{1}=5,\ a_{n}=a_{n-1}+10$

B $a_{1}=3,\ a_{n}=5a_{n-1}$

C $a_{1}=5,\ a_{n}=3a_{n-1}$

D $a_{1}=5,\ a_{n}=a_{n-1}+3$

Question 4

What is the value of $\sum_{k=1}^{4}(5k-1)$?

A $50$

B $46$

C $36$

D $62$

Question 5

Find the sum of the arithmetic series $3+7+11$ that continues with common difference 4 until its last term, 43.

A $506$

B $230$

C $276$

D $253$

Question 6

What is the sum of the first 6 terms of the geometric series $2+6+18+54$ that continues with ratio 3?

A $728$

B $1458$

C $1456$

D $364$

Question 7

An arithmetic sequence begins $4,\,10,\,16$ and ends with 154. How many terms does it have?

A $25$

B $27$

C $26$

D $24$

Question 8

Which sigma expression gives the terms shown in the chart?

Five terms of a series.

A $\sum_{k=1}^{5}5\cdot 2^{k}$

B $\sum_{k=1}^{5}5\cdot 2^{k-1}$

C $\sum_{k=1}^{5}5k$

D $\sum_{k=1}^{4}5\cdot 2^{k-1}$

Question 9

Ethan saves $50 in week 1 and $10 more each week than the week before. How much has he saved in total after 10 weeks?

A $\$1{,}400$

B $\$900$

C $\$1{,}000$

D $\$950$

Question 10

A ball is dropped from 8 feet and rebounds to three-fourths of its previous height on each bounce. How high is the third bounce?

The drop and first three bounces.

A 4.5 ft

B 3.375 ft

C 6 ft

D 2.53 ft

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Arithmetic: explicit $a_{n}=a_{1}+(n-1)d$, recursive $a_{n}=a_{n-1}+d$.
Geometric: explicit $a_{n}=a_{1}r^{n-1}$, recursive $a_{n}=r\cdot a_{n-1}$.
Arithmetic series: $S_{n}=\frac{n(a_{1}+a_{n})}{2}$.
Geometric series: $S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$ for $r\neq 1$.
Sigma notation $\sum_{k=1}^{n}$ is shorthand for adding terms from $k=1$ to $k=n$.