1. what are the next two terms of the following sequence?

1,5,

a: 27, 211

b: 10, 11

c: 12, 15

d: 13, 17

2. what is the common difference of the following arithmetic sequence

102, 100, 98,

a: 2

b: -2

c: -1

d: 102

3. what is the ninth term of the arithmetic sequence defined by the rule below?

a(n( = -14 + (n-1)(2)

a: 232

b: 230

c: 2

d: 4

4. which function below represents the arithmetic sequence

3, 7 , 11,

a: f(n) = 4+3(n-1)

b: f(n) = 4+3n

c: f(n) = 3+4n

d: f(n) = 3+4(n-1)

1.  13, 17                       Option D

2. -2                            Option B

3. 2                             Option C

4. F(n) = 3+4(n-1)        Option D

Step-by-step explanation:

1.  

Given sequence is:   1, 5, 9

Common difference =  5-1 = 9-5 = 4

Next term is :

9+4 = 13

and

13+4= 17

So, next two terms are:  13 & 17.

2.

Given sequence is :

102, 100, 98, 96

Common difference = 100 - 102 = 98 -100 = 96 - 98 = -2

3.

Given rule is :

Aₙ  = -14 + (n - 1)(2)

Find the 9th term

so, we put n = 9

A₉ = -14 + (9-1)*2

A₉ = -14 + 8*2 = -14 + 16

A₉ = 2

Ninth term is 2.

4.

Given sequence is:

3, 7, 11, 15

Write the nth term

Formula is :

F(n) = a₁ + (n-1)d

Where a₁ is first term

n is number of terms

d is common difference

a₁ = 3

d = 7-3 = 11-7 = 15 - 11 = 4

So nth term is :

F(n) = 3 + 4(n-1)

That's the final answer.