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:

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

Step-by-step 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.

Answer 2

The number minus three