Find the recursive formula for the arithmetic sequence −6, 1, 8, 15,...

Question

(1 point)
Responses

a1=−1, an=an−1+17
a1=−1, an=an−1+17

a1=−1, an=an−1+7
a1=−1, an=an−1+7

a1=−1, an=an−1−7

Answer 1

To find the recursive formula for the arithmetic sequence −6, 1, 8, 15,..., we first determine the first term and the common difference.

1. The first term \( a_1 = -6 \).

2. The common difference can be found by subtracting the first term from the second term: \[ d = 1 - (-6) = 1 + 6 = 7. \]

Thus, the common difference \( d = 7 \).

Now we can write the recursive formula:

• The first term: \( a_1 = -6 \).
• The recursive step: \( a_n = a_{n-1} + 7 \) for \( n > 1 \).

So the recursive formula is: \[ \begin{align*} a_1 &= -6, \ a_n &= a_{n-1} + 7 \quad \text{for } n > 1. \end{align*} \]

However, it appears that none of the given response options match the values found above. Please ensure any options given correctly reflect the initial term \( -6 \) and the proper common difference of \( 7 \).