Patterns and Sequences
L . O to find the nth term of a shape and arithmetic sequence.
A sequence is a patterns that involves shapes or numbers that follow a rule.
These online methods will help you tackle questions with ease and get the
Differences of consecutive terms increase by 1 each time so in the next
term you would +5, +6, +7 and so on. The 5th term would be 10+5 =15.
The 6th term would be 15 + 6 = 21.
Also notice these are all triangular numbers.
Differences of consecutive terms increase by 1 each time however in the
next term you would +4, +5, +6 and so on. The 5th term would be 6+4 =10.
The 6th term would be 10 +5 = 15.
Differences of consecutive terms do not increase in a linear fashion,
however notice that the total number are all square numbers.
The 5th term would be 52 = 25
The 6th term would be 62 = 36
In general the nth term of the sequence is denoted by n2.
10th term = 102 = 100
100th term = 1002 = 10000
nth term of an arithmetic series
An arithmetic sequence is where you apply the same rule to each term, which
maybe the difference, or a 2 step rule which involves multiplying by a constant
and then adding another constant.
Here is an arithmetic sequence 5, 8, 11, 14, 17. Find:
- The difference between consecutive terms
- The zero term
- An expression to find the nth term
|Term Number (n)||Output|
The difference is 3
Find the difference between term 2 and term 1.
8 – 5 = 3
Find the difference between term 3 and term 2.
11 – 8 = 3
This step is just to confirm the difference is always the same throughout.
2. The zero term can be found by working backwards. In the sequence if you
add 3 to the output you gain the next term. Here instead of adding 3,
subtract 3 from the first term.
5– 3 = 2 the 0th term
3. Before tackling this part, there is one simple rule you need to know. To
find the nth term of a sequence:
nth term = difference x n + zero term
nth term = 3x n + 2
Check: Term 5 = 17
(3 X 5 ) + 2 = 17!!
The nth term = 3n + 2
Note down the difference and the 0th term (if not done so already and apply
it to the rule )
Double check the nth term you’ve calculated works using an existing term.
Remember to remove any multiplication signs because this is an algebraic