Question

Could someone help me with B

Answer 1

`a_n = 12 - 3n`

Explanation:

The first term is 9.

Term 1 is 9.

Term 2 is 9 - 3.

Term 3 is 9 - 2(3).

Term 4 is 9 - 3(3).

Term 5 is 9 - 4(5)

Notice the pattern in terms 3 through 5. For each term, subtract 1 less than the term number multiplied by 3 from 9.

For term n, you subtract 1 less than n times 3 from 9.

The nth term is 9 - (n - 1) * 3

`a_n = 9 - (n - 1) * 3`

Now we simplify the expression on the right side.

`a_n = 9 - 3(n - 1)`

`a_n = 9 - 3n + 3`

The expression for the nth term is

`a_n = 12 - 3n`

Let's see if it works.

n = 1

`a_n = 12 - 3(1) = 12 - 3 = 9`

n = 2

`a_n = 12 - 3(2) = 12 - 6 = 6`

n = 3

`a_n = 12 - 3(3) = 12 - 9 = 3`

n = 4

`a_n = 12 - 3(4) = 12 - 12 = 0`

n = 5

`a_n = 12 - 3(5) = 12 - 15 = -3`

n = 6

`a_n = 12 - 3(6) = 12 - 18 = -6`

As you can see, following this rule fro the nth term, we got the same first siz terms you got above. Our answer is correct.

Answer:
`a_n = 12 - 3n`