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:

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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