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Grade 8 Number Patterns Quiz 2

Tables, General Rules and Flow Diagrams

What this quiz covers

grade8_patterns_quiz2 draws its questions at random from a bank of 10 questions, with full worked solutions for every one.

Worked examples

A few of the question types, with full solutions, so you know what to expect.

In the sequence \(4;\ 7;\ 10;\ 13;\ \ldots\), what is the term value at position \(n=2\)?

  1. 7
  2. 10
  3. 2
  4. 4

Answer: 7

\(\text{The position number tells us where the term is.}\)

\(\text{Position 1 is 4, position 2 is 7.}\)

What is the general rule for \(4;\ 7;\ 10;\ 13;\ \ldots\)?

  1. \(T_n=3n+1\)
  2. \(T_n=3n\)
  3. \(T_n=n+3\)
  4. \(T_n=4n\)

Answer: \(T_n=3n+1\)

\(\text{The constant difference is } +3\text{, so start with } 3n\)

\(\text{When } n=1\text{: } 3(1)=3\text{, but the first term is 4, so add 1.}\)

\(\text{Check: } T_4=3(4)+1=13\)

Use \(T_n=3n+1\) to find the 50th term.

  1. 151
  2. 150
  3. 153
  4. 16

Answer: 151

\(T_{50}=3(50)+1\)

\(=150+1=151\)

For \(T_n=3n+1\), in which position is the term 100?

  1. 33rd
  2. 34th
  3. 301st
  4. 30th

Answer: 33rd

\(3n+1=100\)

\(3n=99\)

\(n=33\)

Find the rule for \(2;\ 5;\ 8;\ 11;\ \ldots\)

  1. \(T_n=3n-1\)
  2. \(T_n=3n+1\)
  3. \(T_n=2n+3\)
  4. \(T_n=n+3\)

Answer: \(T_n=3n-1\)

\(\text{Constant difference } +3\text{, so start with } 3n\)

\(\text{When } n=1\text{: } 3n=3\text{, but the first term is 2, so subtract 1.}\)

\(\text{Check: } T_4=3(4)-1=11\)