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

a)

b)

Step-by-step 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:  

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

Given:

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:  

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

Given:

See below

Step-by-step explanation:

a) a = 2 and d = 3

= 2 + (n - 1)(3)

= 3n - 1

b) a = 9 and d = 2

= 9 + (n - 1)(2)

= 2n + 7

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step-by-step explanation: