Question

Find the missing terms of the arithmetic sequence.

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
Image with alt text: negative 2 , 3, 8

Answer 1

To find the missing terms in the arithmetic sequence with the given terms of negative 7 and 13, we begin by identifying the common difference of the sequence.

1. **Identify the Known Terms:**
- The first known term is -7.
- The next known term after the missing ones is 13.

2. **Calculate the Number of Steps Between Known Terms:**
- From -7 to 13, there are 4 steps (the missing terms will be in between).

3. **Find the Common Difference:**
- The common difference \( d \) can be found using the formula for arithmetic sequences:
\[
d = \frac{{\text{{last term}} - \text{{first term}}}}{{n - 1}}
\]
where \( n \) is the total number of terms. Here,
- Last term = 13
- First term = -7
- Number of terms (from -7 to 13, including both extremes) = 6.

Substitute into the formula:
\[
d = \frac{{13 - (-7)}}{{6 - 1}} = \frac{{13 + 7}}{{5}} = \frac{{20}}{{5}} = 4.
\]

4. **Find the Missing Terms:**
- Starting from -7, we will add the common difference of 4 incrementally to find the next three missing terms:
- First missing term: -7 + 4 = -3
- Second missing term: -3 + 4 = 1
- Third missing term: 1 + 4 = 5

So, the sequence now reads:
-7, -3, 1, 5, 13.

Now, let's see which response matches the sequence.
- The options given are:
- 8.5, 10, 11.5
- -3, 3, 9
- -4, 2, 6
- -2, 3, 8

None of the provided options directly match the calculated missing terms of -3, 1, and 5.

Therefore, matching these terms, the closest option could be **-3, 3, 9**, but that option does not represent the sequence directly as the arithmetic sequence maintains a consistent gap of 4.

Thus, the answer is:
- Missing terms are -3, 1, and 5, but none of the offered choices match mathematically.