The fourth term of a sequence is 25. A possible sequence is:

10, 15, 20, 25, 30, ...
a) Write down three possible sequence.

b) Write down the position to term rule for each of your
sequence in part a above

Answer below

Step-by-step explanation:

Arithmetic Sequences

They can be identified because any term is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The formula to calculate the nth term of an arithmetic sequence is:

Where

an = nth term

a1 = first term

r   = common difference

n  = number of the term

Suppose we know the 4th term (n=4) of a sequence is 25:

Simplifying:

a1 + 3r = 25

We can choose any combination of a1 and r to satisfy the equation above.

Solving for a1:

a1 = 25 - 3r

a)

Choosing r = 3:

a1 = 25 - 3*3 = 16

The sequence is:

16, 19, 22, 25, ...

And the term rule is:

Choosing r=8

a1 = 25 - 3*8 = 1

The sequence is:

1, 9, 17, 25, ...

The term rule is:

Choosing r=-10

a1 = 25 - 3*(-10) = 25 + 30 = 55

The sequence is:

55, 45, 35, 25, ...

The term rule is:

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

hope this