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Grade 8 Number Patterns Quiz 3

Comprehensive: Patterns, Rules, Tables and Flow Diagrams

What this quiz covers

grade8_patterns_quiz3 draws its questions at random from a bank of 13 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.

Find the next two terms: \(4;\ 9;\ 14;\ 19;\ \ldots\)

  1. \(24;\ 29\)
  2. \(23;\ 27\)
  3. \(24;\ 28\)
  4. \(25;\ 31\)

Answer: \(24;\ 29\)

\(\text{Constant difference } +5\)

\(19+5=24,\quad 24+5=29\)

Find the next two terms: \(2;\ 6;\ 18;\ 54;\ \ldots\)

  1. \(162;\ 486\)
  2. \(108;\ 216\)
  3. \(58;\ 62\)
  4. \(162;\ 324\)

Answer: \(162;\ 486\)

\(\text{Constant ratio } 3\)

\(54\times3=162,\quad 162\times3=486\)

The sequence \(1;\ 4;\ 9;\ 16;\ \ldots\) has:

  1. Neither a constant difference nor a constant ratio
  2. A constant difference of 3
  3. A constant ratio of 4
  4. A constant difference of 5

Answer: Neither a constant difference nor a constant ratio

\(\text{Differences: } 3,\ 5,\ 7 \text{ — not constant.}\)

\(\text{Ratios: } 4,\ 2.25,\ \ldots \text{ — not constant.}\)

\(\text{It is the square-number pattern } n^2\)

Find the rule for \(5;\ 8;\ 11;\ 14;\ \ldots\)

  1. \(T_n=3n+2\)
  2. \(T_n=3n-2\)
  3. \(T_n=5n+3\)
  4. \(T_n=n+3\)

Answer: \(T_n=3n+2\)

\(\text{Constant difference } +3\text{, so } T_n=3n+c\)

\(\text{Use } n=1\text{: } 5=3(1)+c\text{, so } c=2\)

Use \(T_n=4n-1\) to find \(T_{12}\).

  1. 47
  2. 48
  3. 43
  4. 51

Answer: 47

\(T_{12}=4(12)-1\)

\(=48-1=47\)