1. WEEK 1 – LESSON 3 SEQUENCES nth TERM
Angel G. Bassig

2. STARTER Week 1 – Lesson 3 Starter
Please go to our Maths iTunesU course and answer the starter activity for 5 minutes.
Week 1 – Lesson 3 Starter

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

4. Formulae from Sequences
Here are the first five terms of a number sequence . . . 1 2 3 4 5
Position (n) 8 11 14 17 20
Term
To get each term in this sequence, we:
Multiply the position by 3, then add 5
This means that the formula for this sequence is:
3n + 5
Our aim is to find formulae for different sequences

5. the final term, we subtract the difference from the first term
To find a formula for a number sequence we look at the difference between the terms:
Formulae from Sequences 7 11 15 19 23
Difference is the same (4) so the formula starts with 4n
+ 4
+ 4
+ 4
+ 4
To find
the final term, we subtract the difference from the first term
Formula 4n
+ 3 7 -
+ 4
= 3

6. the final term, we subtract the difference from the first term
To find a formula for a number sequence we look at the difference between the terms:
Formulae from Sequences 9 16 23 30 37
Difference is the same (7) so the formula starts with 7n
+ 7
+ 7
+ 7
+ 7
To find
the final term, we subtract the difference from the first term
Formula 7n
+ 2 9 -
+ 7
= 2

7. the final term, we subtract the difference from the first term
To find a formula for a number sequence we look at the difference between the terms:
Formulae from Sequences 2 8 14 20 26
Difference is the same (6) so the formula starts with 6n
+ 6
+ 6
+ 6
+ 6
To find
the final term, we subtract the difference from the first term
Formula 6n
- 4 2 -
+ 6
= -4

8. Answer the following worksheet in pairs
Let’s check your understanding …
Answer the following worksheet in pairs
Time: 10 Minutes

9. For each of the number sequences below, find a rule for the nth term (tn) and work out the value of t100.
Question 1
8, 13, 18, 23, 28,
tn= 5n + 3
t100= 5 x = 503
Question 2
1, 4, 7, 10, 13,
tn= 3n - 2
t100= 3 x = 298
Question 3
2, 9, 16, 23, 30,
tn= 7n - 5
t100= 7 x = 695
9, 15, 21, 27, 33,
tn= 6n + 3
t100= 6 x = 603
Question 4
Question 5
-1, 4, 9, 14, 19,
tn= 5n - 6
t100= 5 x = 494
-3, 1, 5, 9, 13,
Question 6
tn= 4n - 7
t100= 4 x = 393
Question 7
6, 18, 30, 42, 54,
tn= 12n - 6
t100= 12 x = 1194

10. Answer the following worksheet individually.
Let’s check your understanding …
Answer the following worksheet individually.
Time: 10 Minutes

11. Formulae from Sequences
Find the formula for each of these sequences 1. 2. 3. 4. 5. 6. 7. 8.
7, 12, 17, 22,
7, 11, 15, 19,
2, 9, 16, 23,
13, 22, 31, 40,
12, 32, 52, 72,
11, 13, 15, 17,
1, 12, 23, 34,
- 5, 1, 7, 13,
5n + 2
4n + 3
7n - 5
9n + 2
20n - 8
2n + 9
11n 6n

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