Question

the first four terms of a sequence are shown below: 8, 5, 2, −1 Which of the following functions best defines this sequence?

Answer 1

Answer: the answer would be c

Answer 2

`f(1)=8, f(n+1)=f(n)-3`

Explanation:

The given choices are

• f(1) = 8, f(n + 1) = f(n) + 3; for n _ 1
• f(1) = 8, f(n + 1) = f(n) - 5; for n _ 1
• f(1) = 8, f(n + 1) = f(n) + 5; for n _ 1
• f(1) = 8, f(n + 1) = f(n) - 3; for n _ 1

The given sequence is 8, 5, 2, -1,...

Where the first term is 8, the difference is -3, because the sequence is decreasing.

The arithmetic sequence is defined as

`a_(n)=a_(1)+(n-1)d`

Where
`a_(1)=8` and
`d=-3`. So for a general term, the sequence is defined as

`a_(n)=8+(n-1)(-3) \\a_(n)=8-3n+3\\a_(n)=11-3n`

However, notice that the given choices are using another notation, which is an easier notation actually.

`f(1)=8` refers to the first term of the sequence.

We know that the difference is -3, that is, the sequence is made by adding -3 to the first term.

`f(n)` is the n-term and
`f(n+1)` is the follwoing term.

So, notice that to find the following term
`f(n+1)`, we just need to add -3 to the first term
`f(1)=8`.

Therefore, the function that best defines the sequence is

`f(1)=8, f(n+1)=f(n)-3`

So, the right answer is the last choice.