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.
-
Identify the Known Terms:
- The first known term is -7.
- The next known term after the missing ones is 13.
-
Calculate the Number of Steps Between Known Terms:
- From -7 to 13, there are 4 steps (the missing terms will be in between).
-
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: \[ d = \frac{{13 - (-7)}}{{6 - 1}} = \frac{{13 + 7}}{{5}} = \frac{{20}}{{5}} = 4. \]
-
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.
1 answer