To find the missing terms in the arithmetic sequence \(-23, __, __, __, __, __, __, 5\), we first need to determine the common difference \(d\).
The first term \(a_1\) is \(-23\), and the last term \(a_8\) is \(5\). The sequence has 8 terms, so the \(n\)-th term of an arithmetic sequence can be expressed as:
\[ a_n = a_1 + (n - 1)d \]
For the 8th term (\(n = 8\)):
\[ a_8 = a_1 + (8 - 1)d \] \[ 5 = -23 + 7d \]
Now we solve for \(d\):
\[ 5 + 23 = 7d \] \[ 28 = 7d \] \[ d = \frac{28}{7} = 4 \]
Now that we have the common difference \(d = 4\), we can find the missing terms:
- \(a_2 = a_1 + d = -23 + 4 = -19\)
- \(a_3 = a_2 + d = -19 + 4 = -15\)
- \(a_4 = a_3 + d = -15 + 4 = -11\)
- \(a_5 = a_4 + d = -11 + 4 = -7\)
- \(a_6 = a_5 + d = -7 + 4 = -3\)
- \(a_7 = a_6 + d = -3 + 4 = 1\)
Therefore, the completed arithmetic sequence is:
\(-23, -19, -15, -11, -7, -3, 1, 5\)