Question

find the indicated term in each arithmetic sequence.
a_(12) for -17, -13, -9, ...

Answer 1

To find the 12th term (\(a_{12}\)) of the arithmetic sequence given by -17, -13, -9, ..., we first need to determine the first term and the common difference.

1. **Identify the first term (\(a_1\))**:
\[
a_1 = -17
\]

2. **Determine the common difference (\(d\))**:
\[
d = a_2 - a_1 = -13 - (-17) = -13 + 17 = 4
\]

3. **Use the formula for the \(n\)-th term of an arithmetic sequence**:
\[
a_n = a_1 + (n - 1)d
\]

Plugging in \(n = 12\):
\[
a_{12} = a_1 + (12 - 1) \cdot d
\]
\[
a_{12} = -17 + 11 \cdot 4
\]
\[
a_{12} = -17 + 44
\]
\[
a_{12} = 27
\]

Thus, the 12th term (\(a_{12}\)) of the sequence is **27**.