1. Number Sequences – Finding next or missing terms
Mathematics
Number Sequences – Finding next or missing terms

2. Aims of the Lesson To investigate linear number sequences.
To learn how to find the next terms of a linear sequence.
To learn how to find previous or missing terms in a linear sequence.

3. Example
Make chains of matchstick squares and count the number of matches needed
In this sequence we are adding 3 more matches each time, so we are adding 3 on to the last number each time.
[Adding 3 each time will give us a rule connected to the 3 times table.]

4. Describing Rules
There are two ways of describing a rule for sequences…
either relating one term to the next term
or relating a term to its position in the sequence
For the matchstick example…
The term-to-term rule is ADD 3 (to the last term)
The position-to-term rule is MULTIPLY (the position) by 3 then add 1 on

5. Describing Rules (cont’d)
Term-to-term rules are usually described in words (add 3) or using operations and numbers (+3)
Position-to-term rules can be described in words (multiply by 3 then add 1) but are more usually expressed algebraically (i.e. 3n+1)

6. Arithmetic Sequences
First find the common difference – the difference between two consecutive terms (which ONLY works for linear arithmetic sequences).
Use this to find the next or missing values
Remember that if you need to find earlier values than the one shown, you need to do the opposite operation.
E.g. Add 3 going forward becomes subtract 3 going backwards.

7. Examples Find the next 2 terms and the rule for: 2, 5, 8, 11, 14 ….
2  5 gives us the rule of:
[CHECK: 5  8 is also +3]
Number after 14  =
Number after 17  =
Find the missing terms and the rule for: 5, __, 19, 26, __
19  26 gives us the rule of:
Number before 19  19 – 7 =
[CHECK: also gives 12]
Number after 26  =
Add 3 (common diff = +3) 17 20
Add 7 (common diff = +7) 12 33

8. Harder Examples
Find the missing terms and rule for: ___, 27, ___, 19, 15
19  15 gives us the rule of:
Number after 27  27 – 4 =
[CHECK: 23  23 – 4 = 19!]
Number before 27  =
Find the missing terms and rule for: 48, ___, 70 , ___, 92
48  70 (2 jumps!) gives us: Add 22
So our rule for one jump is half this 
Number after 48  =
[CHECK: 59  = 70!]
Number after 70  =
Take 4 (common diff = –4) 23 31
Add 11 (common diff = +11) 59 81

9. REMEMBER Please remember the following:
Always check answers in another way
Use an arrow not an equal sign if the statements on either side are not equal
E.g. 19 =
Should be: 19  = 22
This shows that workings using the 19 were and that these were equal to 22!
(is wrong because 19 does NOT equal 22!)

10. What next?
Make notes (including examples) on finding the next or missing terms in a linear arithmetic sequence.
Work through the MyMaths lesson (and the its online homework) called:
Algebra > Sequences > Arithmetic Sequences
Save and complete the worksheet: LinSeq-S1.xlsx
Now move on the Seq-Nth powerpoint…