Question

Identify the correct recursive formula for the following sequence.

-6, -3, 0, 3, . . .

(1 point)
Responses

a1=−6 and an=an−1+3\(a_1=-6\ and\ a_n=a_{n-1}+3\) - no response given

a1=−6 and an=an−1−3\(a_1=-6\ and\ a_n=a_{n-1}-3\) - incorrect

a1=−6 and an=an−1×(−3)\(a_1=-6\ and\ a_n=a_{n-1}\times\left(-3\right)\) - no response given

a1=−6 and an=an−1×3

Answer 1

To determine the correct recursive formula for the given sequence \(-6, -3, 0, 3, \ldots\), let's analyze the values:

- The first term \(a_1\) is \(-6\).
- The second term \(a_2\) is \(-3\).
- The third term \(a_3\) is \(0\).
- The fourth term \(a_4\) is \(3\).

To find the recursive relationship, we can observe the difference between consecutive terms:

\[
-3 - (-6) = 3
\]
\[
0 - (-3) = 3
\]
\[
3 - 0 = 3
\]

The difference between consecutive terms is consistently \(3\). This means that each term increases by \(3\) from the previous term, which can be expressed recursively.

Thus, the sequence can be represented as:
- \(a_1 = -6\)
- \(a_n = a_{n-1} + 3\) for \(n > 1\).

So the correct recursive formula is:

\[
a_1 = -6 \text{ and } a_n = a_{n-1} + 3
\]

Therefore, the correct response is:
\(a_1 = -6\) and \(a_n = a_{n-1} + 3\).