Download 3 - Burton Borough School

GCSE Maths Starter 12
1. Round 2.865 to 3 decimal places
2. Calculate 2 + 4 × 3
3. What is the order of rotational symmetry of
this shape
4. Find 15 % of £750
𝑥
5
5. Solve = 7
Lesson 12
Sequences and nth term
Mathswatch clip (65/112).
• To list the next term in a sequence (Grade E)
• To write the next diagram or terms of a
sequence given the nth term (Grade D )
• To calculate the nth term(Grade C)
EXTN:
• To calculate the nth term(Grade C)
Linear Number Sequences/Patterns
A linear number sequence is a sequence of numbers that has a constant
difference between adjacent terms. Consider the first five terms of the number
sequence shown:
The difference between adjacent terms is 3.
position 
1st 2nd 3rd
terms 
5, 8, 11, 14, 17,………………..?
difference 
+2
3
3
4th
3
5th................................nth
3
We want to obtain a general rule that gives us the value of any term (nth) in the
sequence as a function of the term’s position.
n
3n
3n ?+ 2
Can you see how the numbers of this sequence are
5
1
3
related to those in the 3 times table?
8
2
6
Adjacent numbers in the 3 times table also differ by 3.
The terms in this sequence are 2 bigger than the
numbers in the 3 times table.
3
9
11
4
12
14
3n + 2
5
15
17
1st 2nd 3rd
4th
5th.........nth
5, 8, 11, 14, 17,…..?
+2
3
3
3
3
3, 7, 11, 15, 19,…..?
-1
4
4
4
= 3n + 2
4
= 4n - 1
n
4n
4n ?- 1
1
4
3
2
8
7
3
12
11
4
16
15
5
20
19
1st 2nd 3rd
4th
5th.........nth
5, 8, 11, 14, 17,…..?
+2
3
3
3
3
3, 7, 11, 15, 19,…..?
-1
4
4
4
4
8, 13, 18, 23, 28,…..?
+3
5
5
5
3n + 2
5
4n - 1
5n + 3
n
5n
5n ?+ 3
1
5
8
2
10
13
3
15
18
4
20
23
5
25
28
1st 2nd 3rd
4th
5th.........nth
5, 8, 11, 14, 17,…..?
+2
3
3
3
3
3, 7, 11, 15, 19,…..?
-1
4
4
4
4
8, 13, 18, 23, 28,…..?
+3
5
5
5
5
-1, 1, 3, 5, 7,…..?
-3
2
2
2
3n + 2
4n - 1
5n + 3
2n - 3
2
1. The common difference tells you the multiple of n required for the first part of
the rule.
2. The second part of the rule is obtained by subtracting the first term and the
common difference.
2a. This is equivalent to asking yourself what you need to do to the common
difference to get to the value of the first term.
Lesson 12
Sequences and nth term
Mathswatch clip (65/112).
Some for you to try..
List the first five terms of each sequence:
1) 8n
2) 3n
3) 3n - 3
4) 5n + 2
5) 7n - 5
Finding the general rule (nth term) of a linear sequence
The terms in this sequence
4,
7,
+3
10,
+3
13,
+3
16,
19,
+3
+3
22,
+3
25, …
+3
can be found by adding 3 each time.
This means that the sequence has 3n as part of the general rule.
4,
1
-3
7,
10,
+3
13,
+3
16,
+3
19,
+3
22,
+3
25, …
+3
To find the next part of the general rule we go back to find the previous term.
So the general rule (nth term) will be
3n + 1
Find the general rule (nth term) of this sequence
The terms in this sequence are:
2,
7,
+5
12,
+5
17,
+5
22,
27,
+5
+5
32,
+5
37, …
+5
can be found by adding 5 each time.
This means that the sequence has 5n as part of the general rule.
2,
-3
-5
7,
12,
+5
17,
+5
22,
+5
27,
+5
32,
+5
37, …
+5
To find the next part of the general rule we go back to find the previous term.
So the general rule (nth term) will be
5n - 3
Lesson 12
Some for you to try
Mathswatch clip (65/112).
For each of the number sequences below, find a rule for the nth term and
work out the value of the 100𝑡ℎ term.
Question 1
8, 13, 18, 23, 28,
5n + 3
n100= 5 x 100 + 3 = 503
Question 2
1, 4, 7, 10, 13,
3n - 2
n100= 3 x 100 - 2 = 298
Question 3
2, 9, 16, 23, 30,
7n - 5
n100= 7 x 100 - 5 = 695
Question 4
9, 15, 21, 27, 33,
6n + 3
n100= 6 x 100 + 3 = 603
Question 5
-1, 4, 9, 14, 19,
5n - 6
n100= 5 x 100 - 6 = 494
Question 6
-3, 1, 5, 9, 13,
4n - 7
n100= 4 x 100 - 7 = 393
Question 7
6, 18, 30, 42, 54,
12n - 6
n100= 12 x 100 - 6 = 1194
Lesson
Mathswatch Clip.
Exam questions