Question: Write a formula for the general term (the nth term) of the arithmetic sequence shown below. Do not use a recursion formula. Then use the formula for $a_n$ to find $a_{20}$, the 20th term of the sequence.
a_1 = -12, d = -6
Part 1 of 2
a_n =
1. **State the problem:** We need to find the formula for the general term $a_n$ of an arithmetic sequence where the first term $a_1 = -12$ and the common difference $d = -6$.
2. **Formula for the nth term of an arithmetic sequence:**
$$a_n = a_1 + (n-1)d$$
This formula gives the value of the nth term directly without recursion.
3. **Substitute the known values:**
$$a_n = -12 + (n-1)(-6)$$
4. **Simplify the expression:**
$$a_n = -12 - 6(n-1)$$
$$a_n = -12 - 6n + 6$$
$$a_n = -6n - 6$$
5. **Final formula for the nth term:**
$$\boxed{a_n = -6n - 6}$$
This is the explicit formula for the nth term of the sequence.
6. **Find the 20th term $a_{20}$:**
$$a_{20} = -6(20) - 6$$
$$a_{20} = -120 - 6$$
$$a_{20} = -126$$
7. **Answer:** The 20th term of the sequence is $\boxed{-126}$.