Algebra 1 Sequences Quiz with Answers – Free PDF

Contents

This algebra 1 sequences quiz asks 10 multiple-choice questions on arithmetic and geometric sequences, and each answer comes with a short explanation.

Ten multiple-choice questions check your skill with sequences: telling arithmetic from geometric, finding terms, writing explicit and recursive formulas, and using sequences to model growth. Choose the one correct answer, then read the explanation to learn from any mistake.

Algebra 1Common Core: F-IF.A.3 · F-BF.A.2 · F-LE.A.2

🎯 Arithmetic and Geometric Sequences – Algebra 1 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

What is the next term of the sequence $5,15,45,135$?

A $405$

B $180$

C $270$

D $675$

Question 2

What is the common difference of the sequence shown?

The first four terms.

A $8$

B $11$

C $3$

D $7$

Question 3

Which explicit formula describes $4,9,14,19$?

A $a_{n}=4+5n$

B $a_{n}=4+5(n-1)$

C $a_{n}=5+4(n-1)$

D $a_{n}=4\cdot 5^{n-1}$

Question 4

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

A $96$

B $192$

C $36$

D $18$

Question 5

Which recursive formula describes $7,3,-1,-5$?

A $a_{1}=7,\ a_{n}=a_{n-1}-4$

B $a_{1}=7,\ a_{n}=a_{n-1}+4$

C $a_{1}=7,\ a_{n}=-4\cdot a_{n-1}$

D $a_{1}=-4,\ a_{n}=a_{n-1}+7$

Question 6

Which statement describes the sequence graphed below?

Four terms of a sequence.

A Arithmetic with $d=2$

B Arithmetic with $d=4$

C Geometric with $r=2$

D Geometric with $r=4$

Question 7

An arithmetic sequence has $a_{3}=10$ and $a_{7}=34$. What is the common difference?

A $8$

B $6$

C $4.8$

D $24$

Question 8

In the arithmetic sequence $2,5,8,11$, which term equals 71?

A The 23rd term

B The 25th term

C The 69th term

D The 24th term

Question 9

A savings account grows 4% each year, as shown.

Account value at the start of years 1 to 3.

What is the value in year 4?

A $560.80

B $560.00

C $624.32

D $562.43

Question 10

A sequence has $a_{1}=2$ and $a_{n}=2\cdot a_{n-1}+1$. What is $a_{4}$?

A $16$

B $11$

C $23$

D $47$

🎉 Quiz complete!

0 / 10

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:

Standards F-IF.A.3, F-BF.A.2 and F-LE.A.2: sequences as functions, explicit and recursive formulas, and modeling with arithmetic and geometric sequences.
Arithmetic: $a_{n}=a_{1}+(n-1)d$; recursive $a_{n}=a_{n-1}+d$.
Geometric: $a_{n}=a_{1}\cdot r^{n-1}$; recursive $a_{n}=r\cdot a_{n-1}$.
Arithmetic sequences grow linearly; geometric sequences grow or decay exponentially.
To identify the type, test consecutive differences first, then consecutive ratios.