• Home
    • Contact
    • Search our Site!
  • Canadian Tests

    Canadian Forces

    CFAT — TAFC

    Citizenship & ESL

    Canadian Citizenship
    CELPIP  —  CAEL

    Dental

    Canadian DAT

    Provincial Achievement and High School

    Cognitive Abilities Test (CCAT)

    Canadian GED

    Alberta Provincial Achievement

    BC Provincial Achievement

     

    Trades

    Trades Entrance

    Canadian Public Service

    PSC Tests

    Canada Post (GAT)

    Canadian Border Services Agency (CBSA OTEE)

    Canadian Firefighter

    Law Enforcement & Security

    BC Police (JIBC)  — Ontario Police (OACP)  — RCMP

    Canada Corrections —  GATB

    Security Guard

  • Public Service Entrance Exams
    • Air Traffic
    • CRA Tests
    • Food Inspection
    • Korn Ferry
    • PSEE (371)
  • Occupations

    Trades

    EIAT — IBEW — Ironworkers
    Red Seal Welder
    Red Seal Carpenter
    Red Seal Plumber

    Medical and Nursing

    PSB HOAE — NLN PAX — More Nursing

    More

    Criticall 911 Dispatch — Mechanical Aptitude — Watson Glaser — Wonderlic Basic Skills

    Firefighters

    CPS Research & Standard & Assoc. (NFST) — Wonderlic Firefighter — Firefighter Practice
  • High School

    Test Help!

    Practice Test Questions – How to Prepare for a test – How to Answer Multiple Choice – How to Study – How to Study — What Students Say

    High School Exams

    CAAT — CHSPE — Canadian GED — Nelson Denny  — TABE — TACHS
    CHSPE Math — GED Math

    Gifted and Talented

    NNAT   —   SCAT   —   NYC Gifted

    The complete guide to multiple choice!

    Discover 15 secret strategies that will raise your score on any multiple choice exam regardless of the subject.

    Learn More >>>

  • Practice
    • Algebra
    • Anatomy & Physiology
    • Basic Math
    • Geometry
    • College Level
      • Congruence
      • Geometric Transformations
      • Graphs of Polynomials
      • Inverse Functions
      • Linear Equations with 2 Variables
      • Logarithms
      • Number Sequence
      • Prime Factors
      • Trigonometry
    • English Grammar
      • Punctuation
      • Spelling
    • Listening Comprehension
    • Logic & IQ
    • Mechanical Comprehension
    • Reading Comprehension
    • Science
    • Social Studies
    • Basic Statistics
    • Situational Judgement Practice Test – Similar to Government of Canada
    • Vocabulary
  • Test Prep
    • How to Answer Multiple Choice
    • How to Prepare for a Test
    • How to Study – The Complete Guide
    • How to Study Math
    • How to Study Science
    • How to Take Notes
    • Test Anxiety Tips!
    • Flash Cards
Complete Test Preparation Inc.
  • Home
    • Contact
    • Search our Site!
  • Canadian Tests

    Canadian Forces

    CFAT — TAFC

    Citizenship & ESL

    Canadian Citizenship
    CELPIP  —  CAEL

    Dental

    Canadian DAT

    Provincial Achievement and High School

    Cognitive Abilities Test (CCAT)

    Canadian GED

    Alberta Provincial Achievement

    BC Provincial Achievement

     

    Trades

    Trades Entrance

    Canadian Public Service

    PSC Tests

    Canada Post (GAT)

    Canadian Border Services Agency (CBSA OTEE)

    Canadian Firefighter

    Law Enforcement & Security

    BC Police (JIBC)  — Ontario Police (OACP)  — RCMP

    Canada Corrections —  GATB

    Security Guard

  • Public Service Entrance Exams
    • Air Traffic
    • CRA Tests
    • Food Inspection
    • Korn Ferry
    • PSEE (371)
  • Occupations

    Trades

    EIAT — IBEW — Ironworkers
    Red Seal Welder
    Red Seal Carpenter
    Red Seal Plumber

    Medical and Nursing

    PSB HOAE — NLN PAX — More Nursing

    More

    Criticall 911 Dispatch — Mechanical Aptitude — Watson Glaser — Wonderlic Basic Skills

    Firefighters

    CPS Research & Standard & Assoc. (NFST) — Wonderlic Firefighter — Firefighter Practice
  • High School

    Test Help!

    Practice Test Questions – How to Prepare for a test – How to Answer Multiple Choice – How to Study – How to Study — What Students Say

    High School Exams

    CAAT — CHSPE — Canadian GED — Nelson Denny  — TABE — TACHS
    CHSPE Math — GED Math

    Gifted and Talented

    NNAT   —   SCAT   —   NYC Gifted

    The complete guide to multiple choice!

    Discover 15 secret strategies that will raise your score on any multiple choice exam regardless of the subject.

    Learn More >>>

  • Practice
    • Algebra
    • Anatomy & Physiology
    • Basic Math
    • Geometry
    • College Level
      • Congruence
      • Geometric Transformations
      • Graphs of Polynomials
      • Inverse Functions
      • Linear Equations with 2 Variables
      • Logarithms
      • Number Sequence
      • Prime Factors
      • Trigonometry
    • English Grammar
      • Punctuation
      • Spelling
    • Listening Comprehension
    • Logic & IQ
    • Mechanical Comprehension
    • Reading Comprehension
    • Science
    • Social Studies
    • Basic Statistics
    • Situational Judgement Practice Test – Similar to Government of Canada
    • Vocabulary
  • Test Prep
    • How to Answer Multiple Choice
    • How to Prepare for a Test
    • How to Study – The Complete Guide
    • How to Study Math
    • How to Study Science
    • How to Take Notes
    • Test Anxiety Tips!
    • Flash Cards

College Level Math

  • Home
  • College Level Math
  • Number Sequence Review Tutorial and Practice Questions

Number Sequence Review Tutorial and Practice Questions

  • Posted by Brian Stocker MA
  • Date June 20, 2014
  • Comments 0 comment

Sequences

A sequence, in mathematics, is a string of objects, like numbers, that follow a pattern. The individual elements in a sequence are called terms.

Number sequence questions as for a particular term in the sequence, which can be calculated or reasons from the pattern.

Number sequences are College Level Math and appear on standardized tests like the Accuplacer and the COMPASS.

Review and Tutorial

 

A sequence of numbers is a set of numbers, but here they are in order. For example, we can represent the set of natural numbers N as a sequence 1, 2, 3,… A sequence can be finite or infinite. In our case of the sequence of the natural numbers, we have an infinite sequence.

If we have a sequence of numbers a1, a2, a3, … we denote that sequence by {an}. We can write, for example, the sequence of natural numbers like this:

an = an-1 + 1 or an+1 = an+1

From this formula, we can see that each number is greater than the previous number by one, which is true for the sequence of the natural numbers.

The first term (member) of the sequence is denoted by a0. So, if we know the first term of the sequence and we know the formula that describes the sequence, we can find any term of that sequence. Even if we know some other member of the sequence, we can find other members.

Let’s solve 2 examples for both cases:

1) If a0 = 2 and an = an-1 – 2, find the 4th member of the sequence {an}.
Let’s find 2nd and 3rd member, which we will use to find the 4th.

a1 = a0 – 2 = 2 – 2 = 0
a2 = a1 – 2 = 0 – 2 = -2
a3 = a2 – 2 = -2 – 2 = -4

So, our 4th member is number -4.

2) If a2 = 4 and an = 2an-1, find the 1st member of the sequence {an}.

a2
 = 2a1 → 4 = 2a1 → a1 = 2
a1 = 2 a0 → 2 = 2a0 → a0 = 1

So, our first member is 1.

Practice Questions

 

1. If a0 = 3 and an =  – an-1 + 3, find a3 of the sequence {an}.

A. 0
B. 1
C. 2
D
. 3

2. If terms of the sequence {an} are represented by an =  an-1/n and a1 = 1, find a4.

A. 1/2
B. 1/4
C. 1/16
D. 1/24

3. If a0 = 1/2 and an = 2an-12 , find a2 of the sequence {an}.

A. 1/2
B. 1/4
C. 1/16
D. 1/24

4. If members of the sequence {an} are represented by an =  (-1)nan-1 and if a2 = 2, find a0.

A. 2
B. 1
C. 0
D. -2

5. If the sequence {an} is defined by an+1 =  1- an and a2 = 6, find a4.

A. 2
B. 1
C. 6
D. -1

6. If members of the sequence {an} are represented by an+1 =  – an-1 and a2 = 3 and, find a3 +  a4.

A. 2
B. 3
C. 0
D. -2

Answer Key

1. A. 0

a0 = 3

an =  – an-1 + 3

a1 =  – a0 + 3 = -3 + 3 = 0

a2 =  – a1 + 3 = 0 + 3 = 3

a3 =  – a2 + 3 = -3 + 3 = 0

 

2. D. 1/24

an =  an-1/n

a1 = 1

a2 =  a1/2 = 1/2

a3 =  a2/3 = (1/2)/3 = 1/6

a4 =  a3/4 = (1/6)/4 = 1/24

 

3. A. 1/2

a0 = 1/2

an = 2an-12

a1 = 2a02 = 2·(1/2)2 = 2·(1/4) = 1/2

a2 = 2a12 = 2·(1/2)2 = 2·(1/4) = 1/2

 

4. D -2

an= (-1)nan-1

a2=2

2=a2= (-1)2a1= a1  ?  a1=2

a1= (-1)1a0

2=- a0

a0=-2

5. C. 6

an+1 =  1 –  an

a2 = 6

a3 = 1 – a2 = 1 – 6 = -5

a4 =  1 –  a3 = 1 – (-5) = 1 + 5 = 6

6. C. 0

an+1 = – an-1

a2 = 3

a3 =  – a2 = -3

a4 =  – a3 = -(-3) = 3

a3 + a4 =  -3 + 3 = 0

Written by: Brian Stocker MA, Complete Test Preparation Inc.
Share
Tweet
Pin
Share
author avatar
Brian Stocker MA

Previous post

Logarithms Review and Practice Questions
June 20, 2014

Next post

Basic Math - Order of Operation Practice & Tutorial
November 27, 2014

You may also like

function
Inverse Functions Practice Questions
29 March, 2019
communication
Listening Comprehension Practice – Solving a Problem
14 October, 2018
Test9
After you take a Practice Test
20 March, 2018

Leave A Reply Cancel reply

Your email address will not be published. Required fields are marked *

College Level Math Practice

How to Solve Logarithms

Number Sequences

Trigonometry

Quadratics

Ratio and Proportion Practice

Inverse Functions

Functions Practice

Geometric Transformations

Graphic Quadratic Functions

Matrix Multiplication Problems

Prime Factors

Congruent Triangles

Graphing Polynomial Functions

Tests with College Level Math

College Placement Math -- ACCUPLACER -- CUNY

Connect! Share!

Share
Tweet
Pin
Share

If you are a volunteer or non-profit organization, we are happy to provide test prep materials at reduced or no cost.  Please contact us with details of your organization.

About
Contact Us
FAQ
Online Practice Courses

Thank you!

With every purchase, you’re helping people all over the world improve themselves and their education. So thank you in advance for supporting this mission with us! Together, we are truly making a difference in the lives of those often forgotten by the system.
Charities that we support

Share
Tweet
Pin
Share

Visit our Test Prep Learning Center

Learning Center
Copyright -- Privacy -- Returns -- Sitemap