The following tables describe arithmetic sequences

(a) what is the common difference of the sequence xn?

(b) what is x8? what is x12?

(c) what is the common difference of the sequence am?

(d) what is a12? what is a15?

a) the common difference is 20

b)

c) the common difference is -13

d)

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is:

We know common difference d= 20, we need to find

Using we can find

So, We have

Now finding

So,

Now finding

So,

c) what is the common difference of the sequence

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is:

We know common difference d= -13, we need to find

Using we can find

So, We have

Now finding , put n=12

So,

Now finding , put n=15

So,