Question

An arithmetic sequence has this recursive formula:

Answer 1

Answer:

The answer is A.  an=8+(n-1)(-6) .

Step-by-step explanation:

Answer 2

Hello!

The recursive rule for an arithmetic sequence: $a_{n} = a_{n-1} + d$.

The explicit rule for an arithmetic sequence: $a_{n}=a_{1} +d(n-1)$.

$a_{n}$ is the value you are trying to find, or simply the answer. :)

$d$ is the common difference of the sequence.

$a_{1}$ is the first term of the sequence.

Given, $a_{1} = 8$ and $a_{n}=a_{n-1} - 6$...

The common difference is -6, and the first term is 8.

Plug these values into the explicit rule for an arithmetic sequence, you get:

$a_{n}=8+(-6)(n-1)$.

Therefore, the answer is A, $a_{n}=8+(n-1)(-6)$.

If you wondered why, $a_{n}=8+(-6)(n-1)$ is equal to $a_{n}=8+(n-1)(-6)$, the Commutative Property of Multiplication states that when two numbers are multiplied together, the answer is the same regardless of the order of the numbers, which makes $a_{n}=8+(-6)(n-1)$ and $a_{n}=8+(n-1)(-6)$ equal to each other.