Recognising special number sequences | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these could be the first four terms in an arithmetic sequence?
- 11, 8, 5, 2, ... ✓
- -7, -1, 1, 7, ...
- 27, 33, 39, 46, ...
- 118, 120, 122, 124, ... ✓
- 5, 10, 20, 40, ...
6, 30, 150, 750, ... are the first four terms in a geometric sequence with common ratio ______.
- '5' ✓
36, 49, 64, 81, ... are the first four terms in a sequence of square numbers. The next term is ______.
- '100' ✓
Which of these are triangular numbers?
- 1 ✓
- 3 ✓
- 6 ✓
- 9
- 12
Select the expression that represents 4 more than $a + 4$ .
- $a + 8$ ✓
- $a + 4 + a + 4$
- $4(a +4)$
- $4a + 4$
- $4a + 8$
Which of these could be the first four terms in a geometric sequence?
- -1, 2, -10, 20, ...
- 2, -4, 8, -16, ... ✓
- 3, 5, 8, 12, ...
- 5, 10, 15, 20, ...
- 10, 30, 90, 270, ... ✓

Exit quiz

The next term in the sequence 8, 2, 10, 12, ... is found by adding the two previous terms. The next term is ______.
- '22' ✓
Which of these could be an arithmetic sequence?
- $76, 99, 122, 145, ...$ ✓
- $-14, -6, 6, 14, ...$
- $12.4, 16.2, 20.1, 23.8, ...$
- ${4\over 3}, {3\over 2}, {5\over 3}, {11\over 6}, ...$ ✓
- ${1\over 8}, {1\over 4}, {1\over 2}, {3\over 4}, ...$
Which of these could be a geometric sequence?
- -108, 36, 12, -4, ...
- 4, -8, 16, -32, ... ✓
- 1000, 200, 40, 8, ... ✓
- 27, 36, 48, 64, ... ✓
- 10, 20, 30, 40, ...
Match the first four terms of each sequence with the rule which could describe it.
- $a , 2a, 4a, 8a, ...$
  
  ⇔
  
  geometric sequence with common ratio 2 ✓
- $a , 2a, 4a, 7a, ...$
  
  ⇔
  
  sequence which starts by adding $a$ with second difference $+a$ ✓
- $2a, 4a, 6a, 8a, ...$
  
  ⇔
  
  linear sequence with common difference $2a$ ✓
- $3a, 3a^2, 3a^3,$ $3a^4, ...$
  
  ⇔
  
  geometric sequence with common ratio $a$ ✓
- $a+1, 2a+2,$ $3a + 3, 4a + 4, ...$
  
  ⇔
  
  linear sequence with common difference $a + 1$ ✓
This sequence starts by adding 5 and has a common second difference of 3. The next term in the sequence is ______.
- '73' ✓
Which of these could be the first four terms of a sequence with a common second difference? (They are called quadratic sequences).
- 5, 8, 11, 14, ...
- 12, 14, 18, 24, ... ✓
- 9, 11, 15, 23, ...
- 4, 7, 11, 16, ... ✓
- 8, 9, 13, 20, ... ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

You can identify an arithmetic sequence by checking for a common difference between terms.
You can identify a geometric sequence by checking for a common ratio between terms.
You can identify a special number sequence if you can identify how to generate the sequence.

Common misconception

After becoming very familiar with arithmetic sequences pupils can find the difference between the first two terms and just assume the sequence is arithmetic.

Explore a large number of geometric and arithmetic sequences and see if pupils can articulate how they check if a sequence is geometric. They might say the terms of the sequence grow more quickly (for some geometric sequences).

Keywords

Arithmetic/linear sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant.
Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
Triangular - A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle