Find the missing terms of the arithmetic sequence.

Question

ellipsis comma negative 7 comma question mark comma question mark comma question mark comma 13 comma ellipsis

(1 point)
Responses

8.5, 10, 11.5
8.5, 10, 11.5

negative 3, 3, 9
Image with alt text: negative 3 , 3, 9

negative 4, 2, 6
Image with alt text: negative 4 , 2, 6

negative 2, 3, 8

Answer 1

To determine the missing terms in the arithmetic sequence given as \( \ldots, -7, ?, ?, ?, 13, \ldots \), we first need to identify the common difference of the sequence.

1. The last term we know is \( 13 \).

2. We can find the common difference \( d \) by setting up the equation for the term before \( 13 \):

   \[ -7 + 4d = 13 \]

   Here, \( 4d \) represents the number of steps from \(-7\) to \(13\).

   Rearranging gives:

   \[ 4d = 13 + 7 = 20 \] \[ d = \frac{20}{4} = 5 \]

With a common difference \( d = 5 \), we can now find the missing terms directly:

• The term after \(-7\): \[ -7 + 5 = -2 \]

• The next term: \[ -2 + 5 = 3 \]

• The term after \(3\): \[ 3 + 5 = 8 \]

So the missing terms in the sequence are \(-2\), \(3\), and \(8\).

Thus, the complete sequence up to \(13\) is:

\[ \ldots, -7, -2, 3, 8, 13, \ldots \]

The correct option from the provided responses is:

negative 2, 3, 8.