Algebra 1 Arithmetic and Geometric Sequences Test with Point Values (PDF)

Algebra 1 math test: Arithmetic and Geometric Sequences – Maths PDF

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This sequences test for Algebra 1 covers arithmetic and geometric sequences (Common Core F-IF.A.3, F-BF.A.1a, F-BF.A.2, F-LE.A.2), with a free PDF to print.

This test checks arithmetic and geometric sequences for Common Core F-IF.A.3, F-BF.A.1a, F-BF.A.2, and F-LE.A.2. It has 9 questions worth 20 points in all, and you have 45 minutes. Write clear steps, because points are awarded for method as well as for the final answer. Leave a few minutes to review.

Time and points

About this test

Grade: Algebra 1
Chapter: Arithmetic and Geometric Sequences
Standards: F-IF.A.3, F-BF.A.1a, F-BF.A.2, F-LE.A.2
Time: 45 minutes
Total: 20 points

Sequences test: questions

Question 1 – Next term [2 pts]

Find the next term of $2, 10, 50, 250$ and name the type of sequence. (1 point)
Find the next term of $30, 24, 18, 12$ and name the type of sequence. (1 point)

Question 2 – Explicit rule [2 pts]

Write an explicit rule for $6, 10, 14, 18$ and find $a_{15}$.

Question 3 – Recursive rule [2 pts]

Write a recursive rule for $100, 90, 80, 70$.

Question 4 – Geometric rule [2 pts]

Write an explicit rule for $2, 6, 18, 54$ and find $a_{5}$.

Question 5 – Two terms given [2 pts]

An arithmetic sequence has $a_{2} = 9$ and $a_{5} = 18$. Write an explicit rule.

Question 6 – Rule from a graph [2 pts]

Graph for question 6.

The graph shows the first four terms of an arithmetic sequence. Write an explicit rule.

Question 7 – Savings plan [3 pts]

Ethan’s savings.

Ethan’s weekly savings form an arithmetic sequence.

Write an explicit rule for week $n$. (1 point)
Find the amount in week 10. (1 point)
Find the first week in which he saves more than $150. (1 point)

Question 8 – Bounce heights [3 pts]

Bounce heights in inches.

A ball’s first three bounces reach 81, 54, and 36 inches.

Find the common ratio. (1 point)
Write an explicit rule. (1 point)
Find the height of the 4th bounce. (1 point)

Question 9 – Compare sequences [2 pts]

Sequence A is $5, 10, 15, 20, $ and sequence B is $5, 10, 20, 40$. Find the 6th term of each and say which sequence grows faster.

Key facts behind this sequences test

Key facts

A sequence is a function whose inputs are the positions 1, 2, 3, and so on.
Arithmetic: add d each time; aₙ = a₁ + (n – 1)d.
Geometric: multiply by r each time; aₙ = a₁ · r^(n-1).
A recursive rule gives each term from the previous term; an explicit rule gives any term directly.
Arithmetic sequences are linear; geometric sequences are exponential.

How to use this sequences test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 1 chapters: Algebra 1 math.

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