Question

Find the recursive formula for the arithmetic sequence −6, 1, 8, 15,... (1 point) Responses a1=−1, an=an−1+7 a1=−1, an=an−1+7 a1=−1, an=an−1+17 a1=−1, an=an−1+17 a1=−1, an=an−1−7

Answer 1

To find the recursive formula for the arithmetic sequence given, we need to identify the first term and the common difference.

The sequence is:
- **First term (a₁)**: -6
- **Second term (a₂)**: 1
- **Third term (a₃)**: 8
- **Fourth term (a₄)**: 15

To find the common difference (d), we subtract the first term from the second term:
\( d = 1 - (-6) = 1 + 6 = 7 \)

So, the common difference \( d \) is 7.

Now we can write the recursive formula:
- The first term is: \( a_1 = -6 \)
- The recursive relation is: \( a_n = a_{n-1} + 7 \) for \( n > 1 \)

Putting this together, the correct recursive formula is:
- \( a_1 = -6 \)
- \( a_n = a_{n-1} + 7 \) for \( n > 1 \)

None of the given responses directly match this. If the options had \( a_1 = -6 \) instead of \( a_1 = -1 \), it would have matched the calculations. Based on the responses provided, it seems there might have been a misunderstanding in the options.

The correct recursive form based on the clear calculations is:

\( a_1 = -6 \)
\( a_n = a_{n-1} + 7 \) for \( n > 1 \)