1. (continuation of Lesson 3)
WEEK 1 – LESSON 4
SEQUENCES nth TERM
(continuation of Lesson 3)
Angel G. Bassig

2. OBJECTIVE
To be able to find the
nth term of a sequence.

3. tn= 2n 2, 4, 6, 8, 10,………………..? Linear Number Sequences/Patterns
The difference between adjacent terms is 2.
difference 
1st 2nd 3rd 4th th nth
position 
2, 4, 6, 8, 10,………………..?
terms 
+ 2 n 2n 1 2 4 3 6 8 5 10
Can you see how the numbers of this sequence are related to those in the 2 times table?
tn= 2n

4. tn= 3n + 2 5, 8, 11, 14, 17,………………..? Linear Number Sequences/Patterns
The difference between adjacent terms is 3.
difference 
1st 2nd 3rd 4th th nth
position 
5, 8, 11, 14, 17,………………..?
terms 
+ 2 n 3n 1 3 2 6 9 4 12 5 15 5 8 11 14 17 ?
3n + 2
Can you see how the numbers of this sequence are related to those in the 3 times table?
tn= 3n + 2

5. 5, 8, 11, 14, 17,…..?
1st 2nd 3rd 4th th nth
tn= 3n + 2
+ 2
3, 7, 11, 15, 19,…..?
tn= 4n - 1
- 1 n 4n 1 4 2 8 3 12 16 5 20 3 7 11 15 19 ?
4n - 1

6. 5, 8, 11, 14, 17,…..?
1st 2nd 3rd 4th th nth
3, 7, 11, 15, 19,…..?
tn= 3n + 2
tn= 4n - 1
+ 2
- 1
8, 13, 18, 23, 28,…..?
tn= 5n + 3
+ 3 n 5n 1 5 2 10 3 15 4 20 25 8 13 18 23 28 ?
5n + 3

7. tn= 3n + 2 tn= 4n - 1 tn= 5n + 3 tn= 2n - 3 5, 8, 11, 14, 17,…..?
5, 8, 11, 14, 17,…..?
1st 2nd 3rd 4th th nth
3, 7, 11, 15, 19,…..?
tn= 3n + 2
tn= 4n - 1
8, 13, 18, 23, 28,…..?
tn= 5n + 3
+ 2
- 1
+ 3
-1, 1, 3, 5, 7,…..?
tn= 2n - 3
- 3
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.

8. Example Question 1
For the number sequence below:
(a) Find the “position to term” rule (b) Use your rule to find the 58th term (t58)
Difference 7  7n
7  2  - 5
2, 9, 16, 23, 30,……
(a) tn= 7n - 5
(b) t58= 7 x = 401
Example Question 2
For the number sequence below:
(a) Find the “position to term” rule (b) Use your rule to find the 75th term (t75)
9, 15, 21, 27, 33,……
Difference 6  6n
6  9  + 3
(a) tn= 6n + 3
(b) t75= 6 x = 453

9. Answer the following worksheets (2 worksheets) in pairs
Let’s check your understanding …
Answer the following worksheets (2 worksheets) in pairs
Time: 10 Minutes

10. Find the nth term of: 3, 5, 7, 9, 11, … 2n + 1 4, 9, 14, 19, 24, …
6, 9, 12, 15, 18, …
1, 5, 9, 13, 17, …
3, 7, 11, 15, 19, …
8, 14, 20, 26, 32, …
4, 10, 16, 22, 28, …
13, 16, 19, 22, 25, …
0, 1, 2, 3, 4, 5, …
2n + 1
5n - 1
3n + 3
4n - 3
4n - 1
6n + 2
6n - 2
3n + 10
n - 1

11. Find the nth term of: 1, 3, 5, 7, 9, … 2n - 1 3, 8, 13, 18, 23, …
5, 8, 11, 14, 17, …
0, 4, 8, 12, 16, …
2, 6, 10, 14, 18, …
7, 13, 19, 25, 31, …
3, 9, 15, 21, 27, …
12, 15, 18, 21, 24, …
0, 2, 4, 6, 8, 10, …
2n - 1
5n - 2
3n + 2
4n - 4
4n - 2
6n + 1
6n - 3
3n + 9
2n - 2

12. Answer the following worksheets (2 worksheets) individually
Let’s check your understanding …
Answer the following worksheets (2 worksheets) individually
Time: 10 Minutes

13. Find the nth term of: 4, 6, 8, 10, 12, … 2n + 2 5, 10, 15, 20, 25, …
7, 10, 13, 16, 19, …
2, 6, 10, 14, 18, …
4, 8, 12, 16, 20, …
5, 11, 17, 23, 29, …
9, 15, 21, 27, 33, …
14, 17, 20, 23, 26, …
0, 3, 6, 9, 12, 15, …
2n + 2 5n
3n + 4
4n - 2 4n
6n - 1
6n + 3
3n + 11
3n - 3

14. Find the nth term of: 4, 6, 8, 10, 12, … 2n + 2 5, 10, 15, 20, 25, …
7, 10, 13, 16, 19, …
2, 6, 10, 14, 18, …
-4, 0, 4, 8, 12, …
15, 12, 9, 6, 3, …
1.5, 2, 2.5, 3, 3.5, …
-2, -5, -8, -11, -14, …
-3, 0, 3, 6, 9 …
17, 14, 11, 8, 5, …
2n + 2 5n
3n + 4
4n - 2
4n - 8
-3n + 18
½n + 1
-3n + 1
3n – 6
-3n + 20

15. PLENARY Discuss the worksheet answers .
Share one or two things learned in today’s lesson.