1. The nth term, Un
Example
If we are given a formula for Un (th nth term) where find the first five terms of the sequence Un = 3n + 1

2. Example
Find the first 5 terms for the sequence 𝑈 𝑛 =3𝑛+1
𝑈 1 =
3 1 +1= 4
𝑈 2 =
3 2 +1= 7
𝑈 3 =
3 3 +1= 10
𝑈 4 =
3 4 +1= 13
𝑈 5 =
3 5 +1= 16
4, 7, 10, 13, 16

3. Example
Find the first 5 terms for the sequence 𝑈 𝑛 =2𝑛+5
𝑈 1 =
2 1 +5= 7
𝑈 2 =
2 2 +5= 9
𝑈 3 =
2 3 +5= 11
𝑈 4 =
2 4 +5= 13
𝑈 5 =
2 5 +5= 15
7, 9, 11, 13, 15

4. Example
Find the first 5 terms for the sequence 𝑈 𝑛 =6𝑛−1
𝑈 1 =
6 1 −1= 5
𝑈 2 =
6 2 −1= 11
𝑈 3 =
6 3 −1= 17
𝑈 4 =
6 4 −1= 23
𝑈 5 =
6 5 −1= 29
5, 11, 17, 23, 29

5. Example
Find the first 5 terms for the sequence 𝑈 𝑛 =8𝑛−3
𝑈 1 =
8 1 −3= 5
𝑈 2 =
8 2 −3= 13
𝑈 3 =
8 3 −3= 21
𝑈 4 =
8 4 −3= 29
𝑈 5 =
8 5 −3= 37
5, 13, 21, 29, 37

6. (a) 𝑈 𝑛 =2𝑛+3 (b) 𝑈 𝑛 =4𝑛−3 (c) 𝑈 𝑛 =7𝑛−4 (d) 𝑈 𝑛 =5𝑛+2 (e) 𝑈 𝑛 =9𝑛−6
Example
For each of the following sequences
write down the first three terms
Find the 20th term
(a) 𝑈 𝑛 =2𝑛+3
(b) 𝑈 𝑛 =4𝑛−3
(c) 𝑈 𝑛 =7𝑛−4
(d) 𝑈 𝑛 =5𝑛+2
(e) 𝑈 𝑛 =9𝑛−6

7. Example
For the sequence with nth term 𝑈 𝑛 =𝑛 𝑛+1
write down the first three terms
Find the 20th term