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

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.