Generating a sequence using a position-to-term rule | Maths

Starter quiz

A term-to term rule describes how to calculate the next term from....
- the constant additive rule
- the multiplier
- the previous term ✓
- the term number
True or false. In the sequence 0, 1, 2, 3, 4, ... the 2nd term is 3.
- True- the third number is '2'
- False- The second number is not '3' ✓
- There is no way of knowing without the term-to-term rule
If the 7 times table start with $1\times 7 = 7$ what is the 100th number in the 7 times table?
- '700' ✓
Here are the first 3 terms in a pictorial sequence. Which of these rules could refer to the number of lines in each term?
- add 2 to the previous term to get the next term
- add 3 to the previous term to get the next term ✓
- add 5 to the previous term to get the next term
- there are 3 lines per section plus 2 for the base. ✓
- there are 5 lines per section
Which of these is an advantage for using a term-to-term rule
- They are easy to use to find the next term in a sequence ✓
- They are easy to use to find any term in a sequence
- They work for all sequences where there is a rule between successive terms ✓
- They are unique, the same rule will always produce the same sequence.
- There is only one term-to-term rule that will work if you know the first 3 term.
Match the sequences with the term-to-term rules.
- -2, -6, -18, -54, ...
  
  ⇔
  
  multiply the previous term by 3 ✓
- -2, -6, -10, -14, ...
  
  ⇔
  
  add $-4$ to the previous term ✓
- -2, -6, -14, -30, ...
  
  ⇔
  
  multiply the previous term by 2 then subtract 2 ✓
- -2, -6, -12, -20, ...
  
  ⇔
  
  add $-4$ , add $-6$ , add $-8$ , ... ✓
- -2, -6, -14, -26, ...
  
  ⇔
  
  add $-4$ , add $-8$ , add $-12$ , ... ✓
- -2, -6, -8, -8, ...
  
  ⇔
  
  add $-4$ , add $-2$ , add 0, ... ✓

Exit quiz

Match up the keywords to their definitions
- term
  
  ⇔
  
  each value or pattern in a sequence ✓
- term-to-term rule
  
  ⇔
  
  describes how to get from one term to the next ✓
- position-to-term rule
  
  ⇔
  
  describes how to calculate the term from the term number ✓
- sequence
  
  ⇔
  
  a succession of values or patterns usually following a rule. ✓
Using the table shown, match the notation to the term.
- $T_1$
  
  ⇔
  
  3 ✓
- $T_2$
  
  ⇔
  
  1 ✓
- $T_3$
  
  ⇔
  
  0 ✓
- $T_4$
  
  ⇔
  
  -2 ✓
The position-to-term rule for a sequence is 'multiply the term number by 5 then subtract 10'. What is the 20th term in this sequence?
- '90' ✓
Which of these is a position-to-term rule for the number of dots in each pattern of this sequence?
- add 6 to the previous term
- multiply the term number by 6 then add 4 ✓
- multiply the term number by 6 then add 10
- Multiply the term number by 10
- Multiply the term number by 10 then subtract 4
Which of these is a position-to-term rule for the sequence 12, 22, 32, 42, 52, ....
- the term number add 10
- multiply the term number by 10
- multiply the term number by 10 then add 2 ✓
- multiply the term number by 12
- multiply the term number by 12 and subtract 2
Work out the 100th term in the constant additive sequence which starts: 13, 21, 29, 37, ... The first few lines of working are shown.
- '805' ✓

Worksheet

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Lesson Details

Key learning points

The position of a term in the sequence is its term number.
The general term can be used to identify a specific term.
The general term can be used to generate a sequence .
The general term can be used to generate any number in the sequence.
The general term can be used to describe a sequence.

Common misconception

The position-to-term rule is the initial term add the common difference.

Once pupils have found the additive pattern get them to write each term as a value add the difference.

Keywords

Position-to-term - A position-to-term rule describes how to generate the term from the term number.