Question

25 POINTS HELP PLEASE! Complete the table and pattern. Determine the common difference. Write the explicit rule.

Answer 1

Answer:

Look below for the answers.

Step-by-step explanation:

What I'm going to do is one of these very carefully and leave the other 2 to you. They follow exactly the same pattern and once you see one of them done, you should be able to do any of them.

Six

Step one

Find the common difference.

Two values on the second line are always together so subtract the higher number one from the lower numbered on.

n = 3 and n = 4 on this question are side by side. That is you have f(4) and f(3)

ALWAYS subrract the lower numbered one from the higher numbered one

d = f(4) - f(3) = 60 - 64 = - 4

Step Two

Find the first term.

The first term is ALWAYS f(1). Always. There is never any kind of exception. f(1) in this case is 72

Step Three

Write the general explicit term

The general formula for the explicit Formula is ALWAYS

tn = first term + (n -1)*d

first term = 72

d = - 4 from above.

Explicit formula = 72 + (n - 1)*(-4) So the fifth term is

Example

t5 = 72 + (5 - 1)*(-4)

t5 = 72 + 4*(-4)

t5 =72 - 16

t5 = 56

Step Four

Write the Recursive formula

It is always in the same formal

tn = t_(n - 1) + (common difference)

tn = t_(n - 1) - 4 in this case

Example

Find t2

t2 = t1 - 4

t2 = 72 - 4

t2 = 68

If you do the other two, you can leave them in my PM and I will mark them.