Question

Write down in terms of n, an expression for the nth term

of the following sequences:
a) 2 5 8 11 14
b) 9 11 13 15 17

Answer 1

a)
`a_n=3n-1`

b)
`a_n=2n+7`

Explanation:

a) From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

14 - 11 = 3

11 - 8 = 3

8 - 5 = 3

5 - 2 = 3

(so the common difference = 3)

General equation of arithmetic sequence:
`a_n=a+(n-1)d`

(where
`a` is the first term and
`d` is the common difference between terms)

Given:

• 
  `a=2`
• 
  `d=3`

`\implies a_n=2+(n-1)3`

`\implies a_n=2+3n-3`

`\implies a_n=3n-1`

b) From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

17 - 15 = 2

15 - 13 = 2

13 - 11 = 2

11 - 9 = 2

(so the common difference = 2)

General equation of arithmetic sequence:
`a_n=a+(n-1)d`

(where
`a` is the first term and
`d` is the common difference between terms)

Given:

• 
  `a=9`
• 
  `d=2`

`\implies a_n=9+(n-1)2`

`\implies a_n=9+2n-2`

`\implies a_n=2n+7`